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Ifax3 + bx+c has a factor of the form x2 + px + 1, show that a--ca = ab.

JEE/Engineering Exams
Maths
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By actual division, we get, ax? +bx+c R(x) -= ax - ap+ x2 + px +1 Remainder polynomial, R(x)=(b-a +ap2)x+c+ap If ax3 + bx+chas a factor of the form x2 +px + 1, then R(x) must be identically zero, if b-a+ap2 = 0 and c+ap =0 Eliminating p from these equations, we get 2 b-a+a or a? - c2 = ab
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