Factoring

**MATNTRNG** · August 9th 2010, 12:00 PM

If one root of the equation 2x^2 + 10x + k = 0 is -2, what is the other root?

**eumyang** · August 9th 2010, 12:10 PM

Plug in -2 for x and solve for k:
$\begin{aligned} 2x^2 + 10x + k &= 0 \\ 2(-2)^2 + 10(-2) + k &= 0 \\ 8 - 20 + k &= 0 \\ -12 + k &= 0 \\ k &= 12 \end{aligned}$

For a quadratic equation $ax^2 + bx + c = 0$ the sum of the two roots (I'll call them r1 and r2) is -b/a:
$\begin{aligned} r_1 + r_2 &= -\frac{10}{2} \\ -2 + r_2 &= -5 \\ r_2 &= -3 \end{aligned}$

So the other root is -3.

**Archie Meade** · August 9th 2010, 12:19 PM

Originally Posted by MATNTRNG

If one root of the equation 2x^2 + 10x + k = 0 is -2, what is the other root?

The roots are

$\displaystyle\huge\frac{-10\pm\sqrt{.....}}{4}$

For one of these to be $-2=-\frac{8}{4}$

$\sqrt{...}=2$

Therefore the other root is

$\displaystyle\huge\frac{-10-2}{4}$

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