Question

Use the discriminant, b2 - 4ac, to determine which equation has complex solutions.

Answer 1

Using the discriminant, the quadratic equation that has complex solutions is given by:

x² + 2x + 5 = 0.

What is the discriminant of a quadratic equation and how does it influence the solutions?

A quadratic equation is modeled by:

y = ax² + bx + c

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

• If $\mathbf{\Delta > 0}$, it has 2 real solutions.

• If $\mathbf{\Delta = 0}$, it has 1 real solutions.

• If $\mathbf{\Delta < 0}$, it has 2 complex solutions.

In this problem, we want a negative discriminant, hence the equation is:

x² + 2x + 5 = 0.

As the coefficients are a = 1, b = 2, c = 5, hence:

$\Delta = 2^2 - 4(1)(5) = 4 - 20 = -16$

More can be learned about the discriminant of quadratic functions at brainly.com/question/19776811

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