Question

Find the quadratic polynomial whose sum of its zeroes (roots) is $-\frac{8}{5}$ and the product of the zeroes (roots) is $\frac{7}{5}$.

• A. $14x^2+7x+5$
• B. $5x^2+8x+7$
• C. $2x^2-8x+7$
• D. $5x^2-8x+7$

Answer 1

The correct option is B

$5x^2+8x+7$

Given that,

Sum of zeroes = $\frac{-8}{5}$

Product of zeroes = $\frac{7}{5}$

Required quadratic polynomial is,

$f\left(x\right)=\left[\right(x^2-\left(sumofroots\right)x+\left(productofroots\right)]$

Substituting the given values we get,

$f\left(x\right)=[x^2-\frac{(-8)}{5}x+\frac{7}{5}]$

$f\left(x\right)=[x^2+\frac{8}{5}x+\frac{7}{5}]$

multiplying by 5 we get

$f\left(x\right)=5x^2+8x+7$

$\therefore$ Required polynomial is $5x^2+8x+7$.