[JEE Advanced 1980] If $x^2+px+1$ is a factor of $ax^3+bx+c$, then
If $x^2+px+1$ is a factor of $ax^3+bx+c$, then
(a) $a^2+c^2=-ab$
(b) $a^2-c^2=-ab$
(c) $a^2-c^2=ab$
(d) none of these
1 Answer
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✓ Vidaara Team
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· 1mo ago
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Correct answer: (c) $a^2-c^2=ab$
Writing $ax^3+bx+c=(x^2+px+1)(ax+k)$ and matching gives $c=-ap$ and $b=(a^2-c^2)/a$, so $a^2-c^2=ab$.
JEE Advanced 1980 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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