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 May 19th, 2015, 12:22 PM #1 Senior Member   Joined: Jan 2015 From: London Posts: 108 Thanks: 2 Extended Factorising Hi can someone help me work out his equation 2x^2 + 7x - 4 = 0 Help Thanks
 May 19th, 2015, 12:27 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Code: factor(2*x^2 + 7*x - 4) in PARI/GP yields Code: [ x + 4 1] [2*x - 1 1] that is, $2x^2+7x-4=(x+4)(2x-1)$.
 May 19th, 2015, 12:31 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 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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