Question

Find the quadratic equation if the sum roots is $-\frac{8}{5}$ and the product of the roots is $\frac{7}{5}$.

• A. $14x^2+7x+5=0$
• B. $5x^2+8x+7=0$
• C. $2x^2-8x+7=0$
• D. $5x^2-8x+7=0$

Answer 1

The correct option is B $5x^2+8x+7=0$

Given:

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

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

Required quadratic equation,

$x^2-\left(Sumofroots\right)x+\left(Productofroots\right)=0$

Substituting the given values, we get

$x^2-\frac{(-8)}{5}x+\frac{7}{5}=0$

$x^2+\frac{8}{5}x+\frac{7}{5}=0$

multiplying by 5, we get

$5x^2+8x+7=0$

$\therefore$ Required quadratic equation is $5x^2+8x+7=0$.