If f(x) = x^2 - 5x + c, for which values of c will f(x) have zero real roots?

1 Answer
Oct 16, 2015

Answer:

For any #c# greater than #25/4#.

Explanation:

A quadratic equation #ax^2+bx+c# has no real roots if its discriminant is strictly negative, where its discriminant is

#Delta = b^2-4ac#.

In your case, #a=1#, #b=-5# and #c# is to be found. So,

#Delta=5^2-4*1*c=25-4c#

We want #25-4c<0#, so #25<4c#. Solving for #c#, we get

#c>25/4#