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2. John and Jivani together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $128$. Form the quadratic equation to find how many marbles they to start with, if John had $x $marbles.
2. John and Jivani together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $128$. Form the quadratic equation to find how many marbles they to start with, if John had $x $marbles.
Class 10 | Maths | quadratic equations
2. John and Jivani together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $128$. Form the quadratic equation to find how many marbles they to start with, if John had $x $marbles.

Solution:

Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x) = ax2 + bx + c$ where a, b, c, ∈ R and a ≠ 0. 

Given,

John and Jilani together have a total of $45 $marbles.

Let John have$ x$ marbles.

So, Jivani will be having $(45 – x) $marbles.

Number of marbles John had after losing $5 $marbles =$ x – 5$

Number of marbles Jivani had after losing $5$ marbles = $(45 – x) – 5 = 40 – x$

Now, according to the question the product of the marbles that they are having now is 128

So,

$(x – 5)(40 – x) = 128$

⇒$ 40x – x2 – 200 = 128$

⇒ $x2 – 45x + 128 + 200 = 0$

⇒$ x2 – 45x + 328 = 0$

Thus the required quadratic equation is $x2 – 45x + 328 = 0$.

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