Question

John and jivanti 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.

Answer 1

Given;-

John and Jivanti together have $45$ marbles.

Let, the number of marbles john had be $=x$

then the number of marbles jivanti had $=(45-x)$

Now,

both of them lost $5$ marbles each

therefore,

The number of marbles johns had$=(x-5)$

The number of marbles jivanti had$=45-x-5$

$=(40-x)$

Now product of the number of marbles$=128$

therefore,

$\Rightarrow (x-5)(40-x)=128$

$\Rightarrow 40x-x^2-200+5x=128$

$\Rightarrow -x^2+45x-200-128=0$

$\Rightarrow x^2-45x+328=0$ [Multiplying by $-1$]

Hence,

The required quadratic equation is $x^2-45x+328=0$