alg2/trig
posted by lisa .
If 4x^2+9=kx, what value of k will produce equal roots?
the answer is 12 but i don't understand how you get it, please help!

4 x ^ 2 + 9 = kx
4 x ^ 2  k x + 9 = 0
Quadratic equation has two real roots, if Discrininant Ä = 0
Ä = b ^ 2  4 * a * c
In this case :
a = 4
b =  k
c = 9
Ä = b ^ 2  4 * a * c
Ä = (  k ) ^ 2  4 * ( 4 ) * 9
Ä = k ^ 2  144 = 0
k ^ 2  144 = 0
k ^ 2 = 144
k = sqrt ( 144 )
k = ± 12
For k =  12
4 x ^ 2 + 9 = k x
not equal becouse left side of equation are positive ( 4 x ^ 2 + 9 ) are allways great of 0 ) ,and right side of equation are negative.
So solution are k = 12 
Quadratic equation has two real equals roots, if Discrininant Ä = 0
Ä = greek letter Delta