Solve Quadratic Equations By Formula
Before viewing this page, it would be helpful to learn how to Solve Quadratic Expressions By Factorizing.
Quadratic equations have a variable with a power of 2 and are in the form:
ax2 + bx + c = 0
In the quadratic equation x2 + 9x + 20 = 0,
a = 1
b = 9
c = 20.
The formula to solve a quadratic equation is:
| x = | –b ± √ | b2 – 4ac |
| 2a | ||
Example One - Solve by Factorization
Factorize and solve x2 + 9x + 20 = 0
Answer:
x2 + 9x + 20 = 0
( x + 4 ) ( x + 5 ) = 0
Either x + 4 = 0 or x + 5 = 0
If x + 4 + 0
x = –4
If x + 5 = 0
x = –5
x = –4 or –5
Example Two - Solve using the Quadratic Formula
Use the quadratic formula to solve x2 + 9x + 20 = 0
Answer:
a = 1
b = 9
c = 20
| x = | –9 ± √ | 92 – (4 × 1 × 20) |
| 2 × 1 | ||
x = –4 or –5
Example Three
Use the quadratic formula to solve x2 – 3x – 40 = 0
Answer:
a = 1
b = –3
c = –40
| x = | +3 ± √ | (–3)2 – (4 × 1 × (–40)) |
| 2 × 1 | ||
x = –5 or 8
Example Four
Use the quadratic formula to solve 3x2 – 11x + 6 = 0
Answer:
a = 3
b = –11
c = 6
| x = | +11 ± √ | (–11)2 – (4 × 3 × 6) |
| 2 × 3 | ||
x = 3 or 2/3
Questions - Solve using the Quadratic Formula
Q1. x2 – 8x + 7 = 0
Q2. x2 – 18x + 81 = 0
Q3. x2 + 3x = 0
Answers:
A1. x = 1 or 7
A2. x = 9
A3. x = 0 or –3
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