Question

Determine the nature of the solution(s) of

5w2 – 2w= -4
A- one real, rational solution
B- two real, irrational solutions
C- two imaginary solutions
D- two real, rational solutions

Answer 1

Explanation:

This is a quadratic equation. We'll find the discriminant, but must first rewrite this equation in standard form:

5w2 – 2w + 4 = -4 + 4, or 5w^2 - 2w + 4 = 0

The coefficients of the w terms are {5, -2, 4}

and so the discriminant b^2 - 4ac is 4 - 4(5)(20) = -396

Because the discriminant is negative, we know that there will be two unequal, complex solutions.