How can you find the coefficients of a monic quadratic when you know only one non-real root?

We know that non-real roots appear in complex conjugate pairs. Hence when we know one root, we know both of them. Then, as we can factorise a quadratic in it's linear factors, we know our quadratic is a constant times the product of x minus the roots. Lastly, as our quadratic is monic, we must have that this constant is 1. Then find the coefficients by expanding the brackets.

Answered by Ward V. Maths tutor

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