LESSON 3 – SOLVING QUADRATIC EQUATIONS
Note: If the product of two numbers is zero, then one or both numbers must be equal to zero.
QUADRATIC EQUATIONS
A Quadratic equation has the form 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where 𝑎 ≠ 0
1. If 𝑎 × 𝑏 = 0, what must be true about the value of a or the value of b?
2. If you have the equation (𝑥 − 3)(𝑥 + 5) = 0. What values of x make the equation true?
Example ① Solve each quadratic equation.
a) (𝑥 + 5)(𝑥 + 2) = 0
b) (3𝑒 + 5)(2𝑒 − 7) = 0
c) 𝑥 2 + 7𝑥 + 12 = 0
d) 2𝑥 2 − 4𝑥 = 0
e) 4𝑥 2 + 3 = 12
f) 4𝑥 2 + 6 = 10𝑥 + 2
g) 16𝑥 2 + 8𝑥 + 1 = 0
Example ③ A rectangle has dimensions 𝑥 + 8 and 𝑥 − 2. Determine the value of x that gives
an area of 24 𝑐𝑚2 .
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Example ④ Write a quadratic equation with roots of − 3 and 7 in:
i) factored form
ii) standard form