Find the discriminant in the expression: b² - 4ac
From a given quadratic equation ax² + bx + c = 0, substitute the values of a, b, and c to the discriminant formula.
If b² - 4ac = 0, the nature of the roots is one real root of multiciplicity 2.
If b² - 4ac > 0 and is a perfect square; there are two distinct real roots, which are rational.
If b² - 4ac > 0 but NOT perfect square, there are two distinct real roots, which is irrational.
If b² - 4ac < 0, there is no real root.
Example:
4x² - 2x = -3
Re-write to:
4x² - 2x + 3 = 0
a = 4; b = -2; c = 3
Discriminant = b² - 4ac
Discriminant =(-2)² - 4 (4)(3)
Discriminant = 4 - 48
Discriminant = - 44
- 44 < 0 Therefore there is no real root.