Question

If the sum and product of roots of a quadratic equation are $-\frac{7}{2}$ and $\frac{5}{2}$ respectively, then the equation is

• A. $2x^2+7x+5=0$
• B. $2x^2-7x+5=0$
• C. $2x^2-7x-5=0$
• D. $2x^2+7x-5=0$

Answer 1

The correct option is A $2x^2+7x+5=0$

Consider the given sum $\left(\frac{-7}{2}\right)$ and product $(-\frac{5}{2})$ of roots of quadratic equation.

We know quadratic equation,

$x^2-$( sum of zeroes)$x$ +( product of zeros)$=0$

$x^2-\left(\frac{-7}{2}\right)x+(-\frac{5}{2})=0$

$x^2+\frac{7}{2}x-\frac{5}{2}=0$

Multiply by $2$ on sides, we get

$2x^2+7x-5=0$

Hence, this is the required equation.