APPROACH!

There is this problem which has intrigued me for days..Please help .

Let p(x) and q(x) be two quadratic polynomials with integer coefficients.Suppose they have a non-rational zero in common.

Show that

p(x) = r * q(x) for some rational number r.

#Algebra #QuadraticEquations

Easy Math Editor

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Comments

It's intriguing you because it is not true.

For example, take $p(x) = (2x-1) ^2$ and $q(x) = (2x-1) ( 3x-1 )$ .

Calvin Lin Staff - 6 years, 4 months ago

Yes , when I started to prove it I also arrived at the same result but I was not sure.Thanks a lot.

Raven Herd - 6 years, 4 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}`	$\boxed{123}$