Question

determine the values of k for which the quadratic equation x^2=kx+9=o

a) 2 equal real roots

b) 2 distinct real roots
can i get help solving this and getting it explained?

Answer 1

Your question deals with the discriminant b^2 - 4ac
if b^2 - 4ac > 0 , you have 2 distinct real roots
if b^2 - 4ac = 0 , you have 1 real roots, (actually 2 equal real roots, but they count as 1)
if b^2 - 4ac < 0 , you have 2 imaginary or complex roots that are the conjugate of each other

So, after you fix your <b>x^2=kx+9=o</b>, run the above test.

Answer 2

I suspect you mean
x^2 + k x+ 9 = 0
x = [ -k +/- sqrt(k^2 - 36) / (2)
for real roots
k^2 - 36 must be >0

now what happens if k = 6 ?