College Algebra & Trigonometry, 2018a

1.5. QUADRATIC EQUATIONS WITH COMPLEX ROOTS 47
1.5 Quadratic Equations with Complex Roots
In Section 1.3, we considered the solution of quadratic equations that had two
real-valued roots. This was due to the fact that in calculating the roots for each
equation, the portion of the quadratic formula that is square rooted (b 2 −4ac, often
called the discriminant) was always a positive number.
For example, in using the quadratic formula to calculate the the roots of the equation
x 2 − 6x +3=0, the discriminant is positive and we will end up with two
real-valued roots:
x 2 − 6x +3=0
a =1,b= −6,c=3
x = −(−6) ± √ (−6) 2 − 4(1)(3)
2 ∗ 1
= 6 ± √ 36 − 12
2
= 6 ± √ 24
2
≈ 6 ± 4.899
2
≈ 6+4.899
2
≈ 6 − 4.899
2
≈ 10.899
2
≈ 1.101
2
≈ 5.449 ≈ 0.551