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Integrated 2: The Discriminant
𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
What is the discriminant?
Greater than Zero
𝑏2 − 4𝑎𝑐 > 0
Equal to Zero
𝑏2 − 4𝑎𝑐 = 0
Less than Zero
𝑏2 − 4𝑎𝑐 < 0
Find the discriminant and use it to determine how many solutions each quadratic equation has
Ex1: 𝑥 2 + 8𝑥 − 3 = 0
Ex2: −𝑥 2 + 2𝑥 = 5 − 2𝑥
Ex3: 9𝑥 2 + 10 = 6𝑥 + 9
Your Turn A:
𝑥 2 + 6𝑥 − 2 = 0
Ex4: 6𝑥 2 = 8
Your Turn B: −3𝑥 2 + 4𝑥 = 3𝑥
Practice Problems
Use the discriminant to determine how many there are to the quadratic equation below
1) −𝑥 2 − 6𝑥 − 8 = 0
2) 𝑥 2 − 9𝑥 − 5 = 5
3) 5𝑥 2 + 3𝑟 = 9𝑥 2 + 5
4) −7𝑥 2 − 8𝑥 = 0
5) −5𝑥 2 + 10𝑥 + 5 = 10
6) −3𝑥 2 + 𝑥 − 3 = 9𝑥 − 6𝑥 2
Mixed Review