Solve real-coefficient quadratic equations that have complex solutions.
Solve a quadratic with a negative discriminant using the quadratic formula
Problem
Apply the quadratic formula to \(x^{2}-4x+8=0\). Compute the discriminant, rewrite its square root using \(i\), divide \(\text{both}~\text{terms}\) by \(2a\), and state the conjugate pair.
Big Picture
What this problem is really about
A negative discriminant turns the quadratic formula’s radical into an imaginary term. We’ll read the signed coefficients, compute the discriminant, handle negative b carefully, rewrite the radical using i, and divide both the real and imaginary numerator terms by the full denominator.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
