Solving equation with two imaginary roots

[lordvoo]

1. -xⁿ2+2(k+2)x-9k=0
Has two imaginary roots, what are the values of k?

Attempted to break it down and use the quadratic formula but wasn't able to do it. Would like a pointer in the right direction of where to begin to solve it.

Thanks

 

[jedishrfu]

look at the quadratic formula and ask yourself:

What is the relationship between the polynomial coefficients to have imaginary roots?

 

[epenguin]

1. -xⁿ2+2(k+2)x-9k=0
Has two imaginary roots, what are the values of k?




Attempted to break it down and use the quadratic formula but wasn't able to do it. Would like a pointer in the right direction of where to begin to solve it.

Thanks

Yes, or I could say just look at that quadratic formula and ask yourself what terms must be real (take it that k is real) and what terms can be imaginary, it is a conceptual question not one of calculation.

Have made one typo? - I suppose that should be maybe

-x² + 2(k+2)x -9k= 0

Check you haven't made another.