Question

Find the sum of roots and product of roots respectively for the polynomial :
$2x^2+x-5=0$

• A. 2, 5
• B. $-\frac{1}{2},\frac{5}{2}$
• C. $-\frac{1}{2},\frac{5}{2}$
• D. $-\frac{1}{2},-\frac{5}{2}$

Answer 1

The correct option is D $-\frac{1}{2},-\frac{5}{2}$

We know that for a quadratic equation $a{x}^2+bx+c=0$
sum of roots = $\frac{-b}{a}$ & product of roots =$\frac{c}{a}$
Comparing $2x^2+x-5=0$ with $a{x}^2+bx+c=0$, we have
a = 2, b = 1, c = -5
Hence, sum of roots =$-\frac{b}{a}$ = $-\frac{1}{2}$
and product of roots =$\frac{c}{a}$ = $\frac{-5}{2}$ = $-\frac{5}{2}$