Solve using quadratic formula x2 – 4x + 3 = 0
Answer
x = 3,1
Solution
x² – 4x + 3 = 0
Use the quadratic formula to find the solutions.
-b ± √b² – 4(ac) ÷ 2a
Substitute the values a = 1, b = -4, and c = 3 into the quadratic formula and solve for x.
4 ± √(-4)² – 4(1 X 3) ÷ 2 X 1
Simplify the numerator
Raise -4 to the power of 2.
x = 4 ± √16 – 4 X 3 ÷ 2
Multiply -4 by 3
x = 4 ± √16 – 12 ÷ 2
Subtract 12 from 16
x = 4 ± √4 ÷ 2
Rewrite 4 as 2²
x = 4 ± √2² ÷ 2
Pull terms out from under the radical, assuming positive real numbers.
x = 4 ± 2 ÷ 2
Simplify x = 4 ± 2 ÷2
x = 2 ± 1
x = 2 + 1 or x = 2 – 1
x = 3 or x = 1
The final answer is the combination of both solutions.
x = 3,1