#1242 · Algebra · Quadratics

Condition for Impossible Roots

If the roots of $a x^{2} + 2 b x + c = 0$ be possible and different, then the roots of $(a + c) (a x^{2} + 2 b x + c) = 2 (a c - b^{2}) (x^{2} + 1)$ will be impossible, and vice versa.

~15 minProof · checked by AIquadratic equationsdiscriminantnature of roots

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 13

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.