Week 7 – Interpreting The Discriminant
The expression, b2 – 4ac, is called the discriminant of the quadratic equation. The discriminant tells us how many solutions an equation has.
The quadratic equation ax2 + bx + c = 0 has:
- two real roots when b2 – 4ac > 0
ex. x2 – 6x + 5 = 0
(-62 ) – 4(1)(5)
36 – 20
= 16
- one real root when b2 – 4ac = 0
ex. x2 – 6x + 9 = 0
(-6)2 – 4(1)(9)
36 – 36
= 0
- no real roots when b2 – 4ac < 0
ex. x2 – 6x + 13 = 0
(-6)2 – 4(1)(13)
36 – 52
= -16