# Discriminant =(

• May 12th 2008, 02:19 AM
xornr89
Discriminant =(
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 AM
angel.white
Quote:

Originally Posted by xornr89
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.

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

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

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

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 AM
SVXX
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.