I need help on this question and quick ><

Find the value ofkfor which5 + 4x - x^2 = k, hasequal roots.

To just lets you's know,k=9.

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- May 12th 2008, 02:19 AMxornr89Discriminant =(
I need help on this question and quick ><

Find the value of**k**for which**5 + 4x - x^2 = k**, has**equal roots**.

To just lets you's know,**k=9**. - May 12th 2008, 02:25 AMangel.white
$\displaystyle -x^2+4x+5 = k$

$\displaystyle -x^2+4x+5-k = 0$

$\displaystyle -(x^2-4x-5+k) = 0$

By completing the square you know you want $\displaystyle (x-2)^2$ which returns $\displaystyle x^2-4x+4$

so $\displaystyle 4=-5+k ~~~~~~\Rightarrow ~~~~~~k=9$

substituting this in you get

$\displaystyle -(x^2-4x-5+9) = 0$

$\displaystyle -(x^2-4x+4) = 0$

$\displaystyle -(x-2)^2 = 0$

$\displaystyle (x-2)^2 = 0$

$\displaystyle \pm (x-2) = 0$

so x-2=0 and -(x-2)=0

Both of these values return x=2, thus they are the same. - May 12th 2008, 05:52 AMSVXX
Alternately we could do this with the discriminant formula..

For equal roots, D = 0.

$\displaystyle x = -b - \frac {\sqrt{D}}{2 \cdot a}$

$\displaystyle x = \frac {-4}{-2}$

So x = 2.

Substituting..

$\displaystyle 5 + 8 - 4 = 9$

k = 9.