Discriminant

Question 1

When b²-4ac > 0 …

Answer 1

• There are two distinct roots (crosses the x axis).

- If you cannot find the roots through factorisation, use the quadratic formula.

Question 2

When b²-4ac = 0 …

Answer 2

• There is a repeated root (touches a point on the x axis)

Question 3

When b²-4ac < 0 …

Answer 3

• There are no real roots (graph doesn’t cross or touch the x axis)

Question 4

Remember to …

Answer 4

SKETCH

Question 5

Find the value of the discriminant for the quadratic equation:
x² - 5x + 3 = 0

Answer 5

b²-4ac = (-5)² - 4(1)(3)
b²-4ac = 25- 12
b²-4ac = 13

Question 6

For what values of p does the equation x² - 2x + p = 0 have equal roots?

Answer 6

b²-4ac = 0 (equal roots = touches, so the discriminant must be equal to 0)
(-2)² - 4(1)(p) = 0
4 - 4p = 0
4 = 4p
p = 1

Question 7

What are the values of a, b and c in the equation:

4x² - 7x + 6 = 0

Answer 7

a = 4
b = -7
c = 6

Remember the signs before the constant!

Question 8

How do you solve quadratic inequalities?

Answer 8

• Use the discriminant to check for any roots
• SKETCH!!
• Identify which part of the graph you’re looking at - above or below the x axis
• If the values are beneath the x axis and between two points, the format would be: -2 < k < 2
• If the values are above the x axis and not between two distinct points, the format would be: k < -2 or k > 2