(i) $2{{x}^{2}}~+~kx~+\text{ }3\text{ }=\text{ }0$ Comparing the given equation with ax2 + bx + c = 0, we get, a = 2, b = k and c = 3 As we know, Discriminant = b2 – 4ac $=\text{ }{{\left( k...
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Solution: Let’s say, the age of one friend be x years. Then, the age of the other friend will be (20 – x) years. Four years ago, Age of First friend = (x – 4) years Age of Second friend = (20 – x –...
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Solution: Let the breadth of mango grove be l. Length of mango grove will be 2l. Area of mango grove $=\text{ }\left( 2l \right)\text{ }\left( l \right)=\text{ }2{{l}^{2}}$ $2{{l}^{2~}}=\text{...
Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2×2 + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0
Solutions: $\left( i \right)\text{ }2{{x}^{2}}~+~kx~+\text{ }3\text{ }=\text{ }0$ Comparing the given equation with $a{{x}^{2}}~+~bx~+~c~=\text{ }0$ , we get, $a~=\text{ }2,~b~=\text{ }k\text{...
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(i) 2×2 – 6x + 3 = 0
$\left( i \right)\text{ }2{{x}^{2}}~~6x~+\text{ }3\text{ }=\text{ }0$ Comparing the equation with $a{{x}^{2}}~+~bx~+~c~=\text{ }0$ , we get a = 2, b = -6, c = 3 a = 2, b = -6, c = 3 As we know,...
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) 2×2 – 3x + 5 = 0 (ii) 3×2 – 4√3x + 4 = 0
(i) Given, $2{{x}^{2}}~\text{ }3x~+\text{ }5\text{ }=\text{ }0$ Comparing the equation with $a{{x}^{2}}~+~bx~+~c~=\text{ }0$ , we get a = 2, b = -3 and c = 5 We know, Discriminant...