Question

If one zero of the polynomial 2x^2+3x+λ is1/2, find the value of λ and other zero.

Answer 1

The sum of the roots of the quadratic equation $ax^2+bx+c=0$ is

$-\frac{b}{a}$ and the product is $\frac{c}{a}$ .

Consider the equation $2x^2+3x+lamda=0$

Let $\alpha$ be the other root/zero. Then, sum of the roots/zeroes is

$\alpha +\frac{1}{2} =\frac{3}{2} \\ \alpha =1$

Also product of the roots/zeroes is

$1*\frac{1}{2} =\frac{lamda}{2} \\ lamda =1$