Find the discriminate of 4x^2+5x=-3 and determine the number of real solutions

Answer 1

We rewrite this as 4x^2 + 5x + 3 = 0

The discriminant is b^2 - 4ac, where the x^2 coefficient is a, the x coefficient is b, and the constant is c.

When it is greater than 0 there are 2 roots, when it equals 0, there is one root, and when it is less than 0, there are no roots.

a = 4, b = 5, and c = 3

b^2 - 4ac = 5*2 - 4 * 4 * 3 = 25 - 48 = -23 < 0

There are no real roots.