Question

Explain how to use the discriminant to determine the number and type of roots of a quadratic equation.

Answer 1

The general form of the quadratic equation is :

$ax^2+bx+c=0$

The discriminant is :

$D=b^2-4\cdot a\cdot c$

And the general solution is :

$x=\frac{-b\pm\sqrt[]{D}}{2\cdot a}$

So, there are 3 situations for D

1. D = 0

So, the roots of a quadratic equation are two similar roots

2. D > 0

so, roots of a quadratic equation are two different roots

3. D < 0

so, roots of a quadratic equation are not real, two comlex roots