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too tedious !

I came across a problem which I am unable to solve.

Let there be a quartic polynomial \(ax^4 + bx^3 + cx^2 + dx + e = 0\), having real coefficients and roots p,q,r,s . Calculate the value of \((1+ p^2)(1 +q^2)(1+r^2)(1+s^2)\). Kindly provide full solutions .

Note by Raven Herd
1 year, 8 months ago

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Hint:- \( f(x) = ax^4 + bx^3 + cx^2 + dx + e = a(x- p)(x-q)(x-r)(x-s) \) What is \( f(i)*f(-i) \)? Siddhartha Srivastava · 1 year, 8 months ago

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@Siddhartha Srivastava Got that. Raven Herd · 1 year, 3 months ago

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@Siddhartha Srivastava You forgot 'a' on RHS. Krishna Sharma · 1 year, 8 months ago

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@Krishna Sharma Ouch. Sorry. Fixed now. Siddhartha Srivastava · 1 year, 8 months ago

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