#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

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.