Question

Consider the equation 3x+x²=-7.What does the value of the discriminant tell us about number of solutions to this equation?

Answer 1

The equation has two complex solutions

Explanation:

First reorder the terms of the equation:

`x^(2) +3x +7 =0`

Then find the discriminant:

`\Delta= b^(2) -4ac\\\Delta= 3^(2) -4*3*7\\\\\Delta= -75\\`

A negative discriminant tells us that the solutions to this equation are complex numbers since there are no real number solutions for negative square roots. In addition, since the discriminant is different than zero, the equation has two complex solutions.