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 .

#Think

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

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 - 6 years ago

You forgot 'a' on RHS.

Krishna Sharma - 6 years ago

Ouch. Sorry. Fixed now.

Siddhartha Srivastava - 6 years ago

Got that.

Raven Herd - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$