SOLUTION: I was givin the following question. The quadratic equation {{{ x^2+kx+k=0 }}} has no real roots for x. 1) Write down the discriminant of {{{ x^2+kx+k }}} in terms of k. 2)

Question 27170: I was givin the following question.
The quadratic equation has no real roots for x.
1) Write down the discriminant of in terms of k.
2) Hence find the set of values that k can take.
If somebody could help me. Thanks
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
has no real roots
that means the roots are imaginary- they involve , which is i.
The quadratic formula is:

where the equation is

but we have

so,
a = 1
b = k
c = k
substitute these in the formula

The discriminant, which is everything under the square root sign,
needs to be negative if the roots are imaginary
that means

factoring

k can't be greater than 4 or equal to 4.
that would make the inequality false

not true
or

not true either
k can't be zero or less than zero either
I would get

not true
or

not true either
so, that means

meaning k is between 0 and 4 but doesn't include 0 or 4.
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