Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. Solution: Given equation, $2{{x}^{2}}-7x+3=0$ $2\left(...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. Solution: Let’s consider that the faster pipe takes $x$ hours to fill the...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. Solution: Let’s consider the length of smaller side of rectangle as $x$ metres...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. Solution: Let’s assume the usual speed of train as $x$ km/hr Then, the increased...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (v) $\sqrt{3}{{x}^{2}}+2\sqrt{2}{x}-2\sqrt{3}=0$ Solution: Given equation, It is...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (iii) $\left( x-1 \right)\left( 2x-1 \right)=0$ Solution: Given equation,...
Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (i) $2{{x}^{2}}-5x+3=0$ Solution: Given equation, $2{{x}^{2}}-5x+3=0$ It is in...
Given equation, $2{{x}^{2}}+x+4=0$ ${{x}^{2}}+x/2+2=0$ ${{x}^{2}}+2\times \frac{1}{2}\times \frac{1}{2}\times x+2=0$ ${{x}^{2}}+2\times \frac{1}{4}\times x+{{\left( \frac{1}{4}...
Solution: Let’s consider the original number of people as ‘a’. Given that, $Rs.9000$ were divided equally among a certain number of persons. Had there been $20$ more persons, each would have got...
Solution: Let the original price of the toy be ‘x’. Given that, when the list price of a toy is reduced by $Rs.2$, the person can buy $2$ toys more for $Rs.360$. The number of toys he can buy at the...
Solution: Let the cost price be assumed as Rs x. Given, the dealer sells an article for $Rs.24$ and gains as much percent as the cost price of the article. It’s given that he gains as much as the...
Solution: Let’s assume the length of the cloth to be ‘a’ meters. Given, piece of cloth costs $Rs.35$ and if the piece were $4m$ longer and each metre costs $Rs.1$ less, the cost remains unchanged....
Solution: ...
Solution: Let’s assume the usual speed of the plane to be x km/hr, Then the increased speed of...
Solution: Let the ongoing speed of person be x km/hr, Then, the returning speed of the person is $= (x + 10) km/hr$ (from the question) Using, speed = distance/ time Time taken by the person in...
Solution: Let’s assume the usual speed of train as x km/hr Then, the increased speed of the train $= (x + 5) km/hr$ Using, speed = distance/ time Time taken by the train under usual speed to...
Solution: Let’s consider the speed of the fast train as x km/hr Then, the speed of the slow train will be $= (x -10) km/hr$ Using, speed = distance/ time Time taken by the fast train to cover $200...
Solution: Let the original speed of train be x km/hr When increased by $5$, speed of the train $= (x + 5) km/hr$ Using, speed = distance/...
Solution: Let the speed of stream be x km/hr Given, speed of boat in still water is $8km/hr$. So, speed of downstream $= (8 + x) km/hr$ And, speed of upstream $= (8 – x) km/hr$ Using, speed =...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (xvii) $4{{x}^{2}}-2\left( k+1 \right)x+\left( k+4 \right)=0$ Solution: The...
Solution: Let the whole number be x. When it is decreased by $20 , (x – 20)$ And, the reciprocal of the whole number is $1/x$ From the given condition, we have $(x – 20) = 69 x (1/x)$ $x(x – 20) =...
Solution: Assume the integer be x. Then its square will be ${{x}^{2}}$ . And given, their sum is $90$ $x+{{x}^{2}}=90$ ${{x}^{2}}+x-90=0$ Solving for x by factorization method, we have...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (xv) $\left( 4-k \right){{x}^{2}}+\left( 2k+4 \right)x+\left( 8k+1 \right)=0$...
Solution: Given, The sides of the two squares are $= x cm$ and $(x + 4)$ cm respectively. The sum of the areas of these squares = $656c{{m}^{2}}$ We know that, Area of the square = side* side So,...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (xiii) $\left( k+1 \right){{x}^{2}}-2\left( 3k+1 \right)x+8k+1=0$ Solution:...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (xi) $\left( k+1 \right){{x}^{2}}+2\left( k+3 \right)x+\left( k+8 \right)=0$...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (ix) $\left( 3k+1 \right){{x}^{2}}+2\left( k+1 \right)x+k=0$ Solution: The...
Solution: Let’s assume that one part is $(x)$, so the other part will be $(29 – x)$. From the question, the sum of the squares of these two parts is $425$. Expressing the same by equation we have,...
Solution: Let the two consecutive be considered as $(x)$ and $(x +1)$ respectively. Given that, The sum of their squares is $85$. Expressing the same by equation we have,...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (vii) $4{{x}^{2}}-3kx+1=0$ Solution: The given equation $4{{x}^{2}}-3kx+1=0$...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (v) $2k{{x}^{2}}-40x+25=0$ Solution: The given equation...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (iii) $3{{x}^{2}}-5x+2k=0$ Solution: The given equation $3{{x}^{2}}-5x+2k=0$...
Quadratic is that type of problem which deals with a variable multiplied by itself- an operation also known as squaring. (i) $k{{x}^{2}}+4x+1=0$ Solution: The given equation $k{{x}^{2}}+4x+1=0$ is...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: Given, $2$ is as root of $3{{x}^{2}}+px-8=0$ So, on substituting...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: Given, $-5$ is as root of $2{{x}^{2}}+px-15=0$ So, on...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: The given equation $\left( 2p+1 \right){{x}^{2}}-\left( 7p+2...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: The given equation $\left( 3k+1 \right){{x}^{2}}+2\left( k+1...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: Given, ${{x}^{2}}+kx+4=0$ It’s of the form of $a{{x}^{2}}+bx+c=0$...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Solution: Given, $\left( 4-k \right){{x}^{2}}+\left( 2k+4x \right)+\left(...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (i) $k{{x}^{2}}+2x+1=0$ Solution: Given, $k{{x}^{2}}+2x+1=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (v) $kx\left( x-3 \right)+9=0$ Solution: Given, $kx\left( x-3 \right)+9=0$...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (iii) ${{x}^{2}}-4kx+k=0$ Solution: Given, ${{x}^{2}}-4kx+k=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (i) $2{{x}^{2}}+kx+3=0$ Solution: Given, $2{{x}^{2}}+kx+3=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (iii) $\left( k+1 \right){{x}^{2}}-2\left( k-1 \right)x+1=0$ Solution:...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (i) ${{x}^{2}}-2\left( k+1 \right)x+{{k}^{2}}=0$ Solution: Given,...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (v) $3{{x}^{2}}+2x+k=0$ Solution: Given, $3{{x}^{2}}+2x+k=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (iii) $2{{x}^{2}}-5x-k=0$ Solution: Given, $2{{x}^{2}}-5x-k=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. (i) $2{{x}^{2}}+3x+k=0$ Solution: Given, $2{{x}^{2}}+3x+k=0$ It’s of the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Important Notes: – A quadratic equation is in the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Important Notes: – A quadratic equation is in the...
Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring. Important Notes: – A quadratic equation is in the...
$10x – 1/x = 3$ Solution:- $10x – 1/x = 3$ $(10x-1)/x=3$ By cross multiplication we get, $10{{x}^{2}}-1=3x$ $10{{x}^{2}}-3x-1=0$ Divided by $10$ for both side of eachterm we get,...
Solution: - ${{x}^{2}}-(\sqrt{3}+1)x+\sqrt{3}=0$ ${{x}^{2}}-\sqrt{3x}-x+\sqrt{3}=0$ Take out common in each term, $x(x-\sqrt{3})-1(x-\sqrt{3})=0$ $(x-\sqrt{3})(x-1)=0$ Equate both to zero, ...
Solution: - ${{x}^{2}}-(\sqrt{2}+1)x+\sqrt{2}=0$ ${{x}^{2}}-x-\sqrt{2}x+\sqrt{2}=0$ Take out common in each term, $x(x-1)-\sqrt{2}(x-1)=0$ $(x-1)(x-\sqrt{2})=0$ Equate both to zero,...
Solution: - ${{a}^{2}}{{x}^{2}}-3abx+2{{b}^{2}}=0$ Divided by${{a}^{2}}$ for both side of each term we get, ${{a}^{2}}{{x}^{2}}/{{a}^{2}}-3abx/{{a}^{2}}+2{{b}^{2}}/{{a}^{2}}=0$...
Solution: - $\sqrt{2}{{x}^{2}}-3x-2\sqrt{2}$ Divided by $\sqrt{2}$for both side of each term we get, $\sqrt{2}{{x}^{2}}/\sqrt{2}-3x/\sqrt{2}-2\sqrt{2}/\sqrt{2}=0$ ${{x}^{2}}-3x/\sqrt{2}-2=0$...
Solution: - $2/{{x}^{2}}-5{{x}^{2}}/x+2{{x}^{2}}=0$ Multiply by ${{x}^{2}}$for both side of each term we get, $2{{x}^{2}}/{{x}^{2}}-5{{x}^{2}}/x+2{{x}^{2}}=0$ $2-5x+2{{x}^{2}}=0$ Above equation can...
$25x(x+1)=-4$ Solution:- $25x(x + 1) = -4$ Divided by \[25\]for both side of each term we get, \[25{{x}^{2}}/25\text{ }+\text{ }25x/25\text{ }=\text{ }\text{ }4/25\] \[{{x}^{2}}~+\text{ }x\text{...
\[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{25x}\text{ }+\text{ }\mathbf{42}\text{ }=\text{ }\mathbf{0}\] Solution:- \[3{{x}^{2}}~+\text{ }25x\text{ }+\text{ }42\text{ }=\text{...
\[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~-\text{ }\mathbf{13x}\text{ }-\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{0}\] Solution:- \[4{{x}^{2}}~-13x\text{ }-12\text{ }=\text{ }0\] Divided by \[4\]for...
\[\mathbf{5}{{\mathbf{x}}^{\mathbf{2}}}~-\mathbf{11x}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\] Solution:- \[5{{x}^{2}}~-\text{ }11x\text{ }+\text{ }2\text{ }=\text{ }0\]...
\[\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}~-\text{ }\mathbf{x}\text{ }-\text{ }\mathbf{6}\text{ }=\text{ }\mathbf{0}\] Solution:- \[2{{x}^{2}}~-x\text{ }-\text{ }6\text{ }=\text{ }0~~~~~~\] Divided by...
\[\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3x}-\mathbf{9}\text{ }=\text{ }\mathbf{0}\] Solution:- \[2{{x}^{2}}-3x-9\text{ }=\text{ }0\] Divided by \[2\]for both side of each term we get,...
Solution: Given, \[{{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{2}\left( \mathbf{k}\text{ }+\text{ }\mathbf{1} \right)\mathbf{x}\text{ }+\text{ }{{\mathbf{k}}^{\mathbf{2}}}~=\text{ }\mathbf{0}\] It’s...
\[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{16x}\text{ }=\text{ }\mathbf{0}~~~~~~\] Solution:- \[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{16x}\text{ }=\text{...
$(2x + 3) (3x – 7) = 0$ Solution:- $(2x + 3) (3x – 7) = 0$ Equate both to zero, $(2x + 3) = 0, (3x – 7) = 0$ $2x = -3$, $3x = 7$ $x = -3/2$ Or $x = 7/3$
$(x – 8) (x + 6) = 0$ Solution:- $(x – 8) (x + 6) = 0$ Equate both to zero, $(x – 8) = 0, (x + 6) = 0$ $x = 8$ or $x =...
(i) All circles are ____________ (congruent, similar). (ii) All squares are ___________ (similar, congruent). (iii) All ____________ triangles are similar (isosceles, equilaterals). (iv) Two...