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May 19th, 2015, 12:22 PM   #1
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Extended Factorising

Hi can someone help me work out his equation

2x^2 + 7x - 4 = 0

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May 19th, 2015, 12:27 PM   #2
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factor(2*x^2 + 7*x - 4)
in PARI/GP yields
[  x + 4 1]

[2*x - 1 1]
that is, $2x^2+7x-4=(x+4)(2x-1)$.
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May 19th, 2015, 12:31 PM   #3
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Any rational roots are of the form $a \over b$ where $a \in \{\pm1, \pm2, \pm4\}$ and $b \in \{\pm1, \pm2\}$ (these are the integer factors of the units term and the squared term respectively).

That means that a rational root $r$, (if it exists) is one of $\left\{ \pm\frac12, \pm1, \pm2, \pm 4\right\}$. You can test each of these using the factor theorem.

Last edited by v8archie; May 19th, 2015 at 12:36 PM.
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