Which of the following polynomials has solutions that are not real numbers?
a)x^2-6x+3
b)x^2+4x+3
c)-x^2-9x-10
d)x^2+2x+3

D) .

Step-by-step explanation:

All four polynomials are quadratic, meaning that the highest power of the unknown in the equation is two.

The sign of the quadratic discriminant, , is a way to tell if a quadratic polynomial comes with non-real solutions.

There are three cases:

How to find the quadratic discriminant?

If the equation is in this form:

,

where a, b, and c are real numbers (a.k.a. "constants.")

Quadratic discriminant:

.

Polynomial in A:

.

.

. There will be no non-real solutions and two distinct real solutions.

Try the steps above for the polynomial in B, C, and D.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225