Question

use the discriminant to determine whether the following equations have solutions that are: tow different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. 25x^2=10x-1

Answer 1

25x^2 - 10x + 1 = 0

discriminant = b^2 - 4ac = 100-100 = 0

so, the roots are the same.

(5x-1)(5x-1)

Why does the discriminant determine how many roots? Well, the roots are basically -b/2a +/- the discriminant. So, if the discriminant is zero, both roots are -b/2a

If the discriminant is positive, both roots are the same distance away from -b/2a

If the discriminant is negative, there is no real square root, and we have complex roots.