Solve real-coefficient quadratic equations that have complex solutions.
Classify any quadratic using the discriminant
Problem
For \(x^{2}+4x+8=0\), calculate the discriminant \(b^{2}-4ac\) and use its sign to classify the number and type of solutions over the complex numbers.
Big Picture
What this problem is really about
The discriminant classifies a quadratic’s roots before the roots themselves are calculated. We’ll read the signed coefficients, substitute them carefully into b squared minus four a c, evaluate its sign, translate that sign into a root type over the complex numbers, and confirm with the quadratic formula.
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