What is a discriminant and how do I do this?

Question

Use the discriminant to find the number of real solutions of the equation 3x^2 – 5x + 4 = 0. 

Answer 1

The discriminant of Ax² + Bx + C = 0 is B² - 4AC.   Assuming that A, B, C are rational numbers, then:

 

If the discriminant is negative, then the quadratic has 2 imaginary roots.

 

If the discriminant is zero, then the quadratic has 1  rational root.

 

If the discriminant is positive and a perfect square, then the quadratic has 2 rational roots.

 

If the discriminant is positive and not a perfect square, then the quadratic has 2 irrational roots.

 

In the given example, B² - 4AC = (-5)² - 4(3)(4) = 25 - 48 < 0

 

So, the quadratic equation has 2 imaginary roots.   

Answer 2

A discriminant is for an equation in the form ax² + bx + c = 0,

 

the discriminant = b² - 4*a*c

 

(where a, b, and c are the coefficients).