Question

Find the discriminant and the number of real roots for this equation.
x^2 + 3x + 8 = 0

A. 32; two real roots
B. -23; one real root
C. 32; one real root
D. -23; no real roots

Answer 1

I wrote it down, sorry if it’s a little bit messy.

Answer 2

The correct option regarding the discriminant and the number of real roots for this equation is given by:

D. -23; no real roots

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

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

• If $\mathbf{\Delta > 0}$, and it is a perfect square, it has 2 real solutions.

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

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

In this problem, the function is:

x² + 3x + 8.

Hence the coefficients are a = 1, b = 3, c = 8, and the discriminant is given by:

$\Delta = b^2 - 4ac = 3^2 - 4(1)(8) = -23$

Negative discriminant, hence no real roots, and option D is correct.

More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811

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