Question

Find the equation in the from ax^2+bx+c=0 whose sum and product roots are respectively 3/2, —5/2.

Answer 1

By Vieta's formula for a quadratic polynomial we have

$$x_1+x_2=-\dfrac{b}{a}$$

$$x_1\cdot x_2=\dfrac{c}{a}$$

Given

$$x_1+x_2=\dfrac{3}{2}=-\dfrac{b}{a}$$

$$x_1\cdot x_2=-\dfrac{5}{2}=\dfrac{c}{a}$$

Let $a=2.$ Then $b=-3, c=-5.$

The equation is

$$2x^2-3x-5=0$$