This week in Precalculus 11, we learned about interpreting the discriminant.
Discriminant/Radicand: the number underneath a radical sign (√)
Real root: square root of a positive number
In the quadratic formula, the discriminant is – 4ac. By solving the discriminant, we can indicate how many real roots the equation has.
If – 4ac > 0, the equation has 2 real roots.
Example: 5 – 9x + 4 = 0
– 4ac
= – 4(5)(4)
= 81 – 20 · 4
= 81 – 80
= 1 -> 2 real roots
If – 4ac = 0, the equation has 1 real root.
Example: 2 + 16x + 32 = 0
– 4ac
= – 4(2)(32)
= 256 – 8 · 32
= 256 – 256
= 0 -> 1 real root
If – 4ac < 0, the equation has 0 real roots.
Example: 6 + 7 = 0
– 4ac
= – 4(6)(7)
= 0 – 24 · 7
= 0 – 168
= -168 -> 0 real roots
By interpreting the discriminant beforehand, we can determine whether or not to bother solving a quadratic equation.