SOLUTION: For what real values of a does the quadratic 4x^2 + ax + 25 have non-real roots? Give your answer as an interval.

Question 1075729: For what real values of a does the quadratic 4x^2 + ax + 25 have non-real roots? Give your answer as an interval.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The quadratic formula says that the roots are:

when the equation has the form:

They decided that ( a little confusing )
so the list is:

Now I can say:

The roots will be non-real ( imaginary ) whenever
is negative. ( this is called the discriminant )
So I can say:

and also:

Putting these together:

------------------------
example:
satisfies the conditions, so

and also:

Here is the plot when

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