Question

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

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

Answer 1

The correct option is C

$-\frac{1}{2},-\frac{5}{2}$

We know that sum of roots $=\frac{-b}{a}$ & product of roots $=\frac{c}{a}$ for quadratic equation $a{x}^2+bx+c=0$
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 $=\frac{c}{a}=\frac{-5}{2}=-\frac{5}{2}$