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.