A quick way to figure out the number of real roots of an equation The Discriminant A quick way to figure out the number of real roots of an equation

Discriminant? All it is: the thing under the radical in the quadratic formula Discriminant, d = b2 – 4ac Why do we care: If we are only concerned with real roots, this can expedite matters. Easy because you can do this while in the quadratic formula, so it doesn’t add any steps to the process, just a checkpoint.

Using the Discriminant d = b2 – 4ac If d > 0, two real roots If d = 0, 1 real root If d < 0, no real roots That’s all.

Example 1 x2 + 2x = 12 + 3x First, get in quadratic form b = -1 c = -12

Example 2 x2 – 12x + 36 = 0 a = 1 b = -12 c = 36

Example 3 5 x2 – 8x + 9 = 0 a = 5 b = -8 c = 9