Question

The sum of roots and product of roots respectively for the polynomial $2x^2+x-5=0$ are and .

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

Answer 1

Answer: (A), (D)

The correct options are
A -$\frac{1}{2}$
D -$\frac{5}{2}$

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 $=\frac{c}{a}$ $=\frac{-5}{2}$ $=-\frac{5}{2}$