If one root of the quadratic equation x^2-6x+k=0 is the square of the other root , find the value of k

"If one root of the quadratic equation x^2-6x+k=0 is the square of the other root , find the value of k"

As follows:

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Let r be the lesser root and r^2 be the greater.......the sum of the roots   = -b/a  = -[-6] / 1  = 6

So we have that

r^2 + r  = 6     →    r^2 + r - 6 = 0      

Factor

(r + 3) (r - 2)   = 0  

So r = -3    or   r = 2

Then r^2  = 9     or r^2  =4

And the product of the roots =  c/a   =  k/a  = k

So....k =   (-3)(9)   = -27     or k = (2)(4)  = 8

Check

x^2 - 6x - 27  = 0      factors as  (x + 3)(x - 9) = 0     and  the roots are -3 and 9

x^2 - 6x + 8  = 0      factors as (x -2) (x - 4) =0      and the roots are 2 and 4