Worked examples
Two examples
Example 1
Use the quadratic formula to solve: x2 − 2x − 8 = 0
- a = 1, b = −2, c = −8. b2 − 4ac = 4 + 32 = 36, and √36 = 6.
- x = (2 ± 6) ÷ 2: that is 4 or −2.
Answer: x = 4 or x = −2
Example 2
Use the quadratic formula to solve: 2x2 + 3x − 2 = 0
- a = 2, b = 3, c = −2. b2 − 4ac = 9 + 16 = 25, and √25 = 5.
- x = (−3 ± 5) ÷ 4: that is 12 or −2.
Answer: x = 12 or x = −2
Where this is taught: Quiz 40: Quadratic Equations, “The quadratic formula”
The drill
Ten problems
How many:
Type both answers with a comma between them, like 1/2, -2. Fractions are fine. Then press Check my answers at the bottom.Write the numbers on the line. The answer key, with the reasoning, is on the last page.