1. ## Real Roots

(i) Find the range of values of k for which the equation
x^2-4x+k=5kx-4 has real roots

(ii) Hence, deduce, giving a reason, the relationship about the curve
y=(x-1)^2 and the line y=-5x-4

I've solved part (i), the range is k>=0 or k<= -36/25

I can't deduce the relationship for part (ii). Can anyone help??
Thanks!!!!

2. Originally Posted by acc100jt
(i) Find the range of values of k for which the equation
x^2-4x+k=5kx-4 has real roots

(ii) Hence, deduce, giving a reason, the relationship about the curve
y=(x-1)^2 and the line y=-5x-4

I've solved part (i), the range is k>=0 or k<= -36/25

I can't deduce the relationship for part (ii). Can anyone help??
Thanks!!!!
the first part should be k <=0 or k >= 36/25

that is, $\displaystyle (- \infty , 0] \cup [ 36/25, \infty)$

3. Originally Posted by acc100jt
(i) Find the range of values of k for which the equation
x^2-4x+k=5kx-4 has real roots

(ii) Hence, deduce, giving a reason, the relationship about the curve
y=(x-1)^2 and the line y=-5x-4
Are you sure part i) isn't
x^2 - 2x + k = 5kx - 4

In that case you would be using k = 1...

-Dan

4. thanks....topsquark
I guess you are right. I did suspect that there is something wrong with the question