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

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- Aug 9th 2010, 12:00 PMMATNTRNGFactoring
If one root of the equation 2

*x*^2 + 10*x*+*k*= 0 is -2, what is the other root? - Aug 9th 2010, 12:10 PMeumyang
Plug in -2 for x and solve for k:

$\displaystyle \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 $\displaystyle ax^2 + bx + c = 0$ the sum of the two roots (I'll call them r1 and r2) is -b/a:

$\displaystyle \begin{aligned}

r_1 + r_2 &= -\frac{10}{2} \\

-2 + r_2 &= -5 \\

r_2 &= -3

\end{aligned}$

So the other root is -3. - Aug 9th 2010, 12:19 PMArchie Meade