Question

$\text{Find the sum and product of roots of the}\text{polynomial}2x^2+x-5=0.$

• 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 $-\frac{1}{2},-\frac{5}{2}$

$\text{We know that, for a quadratic}\text{equation}a{x}^2+bx+c=0,\text{Sum of roots =}\alpha +\beta \text{and product of roots =}\alpha \beta \text{where}\alpha \text{and}\beta \text{are the roots of the}\text{equation.}$

$\text{Also,}\alpha +\beta =\frac{-b}{a}\text{and}\alpha \beta =\frac{c}{a}$

$\text{On comparing}2x^2+x-5=0\text{with}\text{standard form of quadratic equation}a{x}^2+bx+c=0,\text{we get}a=2,b=1,c=-5$

$\Rightarrow \alpha +\beta =\frac{-b}{a}=-\frac{1}{2}$

$\Rightarrow \alpha \beta =\frac{c}{a}=-\frac{5}{2}$