# Rational Zero

• Nov 9th 2009, 11:16 PM
flexus
Rational Zero
list all possible rational zeros of f.

f(x)=3x^4 + 4x^3 -5x^2 -8
• Nov 10th 2009, 01:22 AM
Bacterius
Do you know what a rational zero is ? It actually is a non-complex root of the equation. Let us solve $f(x) = 0$ :

$3x^4 + 4x^3 -5x^2 -8 = 0$

Can you solve it now ?
• Nov 10th 2009, 02:02 AM
CaptainBlack
Quote:

Originally Posted by Bacterius
Do you know what a rational zero is ? It actually is a non-complex root of the equation. Let us solve $f(x) = 0$ :

$3x^4 + 4x^3 -5x^2 -8 = 0$

Can you solve it now ?

WRONG!, that would make $\sqrt{2}$ a rational zero of $x^2-2$

A rational number is a number that can be written as the ratio of two integers.

This question is meant to be addressed using the rational root theorem, which tells you that any rational root of a polynomial equation with integer coefficients is the ratio of a factor of the constant term to a factor of the coefficient of the highest power occuring.

So for:

$3x^4 + 4x^3 -5x^2 -8 = 0$

the rational roots are amoung $\pm1,\ \pm 2,\ \pm 4,\ \pm 8,\ \pm1/3,\ \pm 2/3,\ \pm 4/3,\ \pm 8/3$

You try each of these to find which are actual roots.

CB
• Nov 10th 2009, 02:07 AM
Bacterius
Aah

Sorry sorry ! Here, a thanks to forgive me (Nod)