Question

compute the discriminant. then determine the number and type of solutions of the given equation
$3x^2 - 3x + 3 = 0$

what is the discriminant?
-27 (simplify your answer.)

choose the sentence that describes the number and type of solutions of the quadratic equation.

a. there are two unequal real solutions
b. there is one real solution.
c. there are two imaginary solutions.
d. there are an infinite number of real solutions.

Explanation:

Step1: Identify quadratic coefficients

For $3x^2 - 3x + 3 = 0$, $a=3$, $b=-3$, $c=3$

Step2: Compute discriminant

Use formula $\Delta = b^2 - 4ac$
$\Delta = (-3)^2 - 4(3)(3) = 9 - 36 = -27$

Step3: Classify solutions

Discriminant $\Delta < 0$, so two imaginary solutions.

Answer:

The discriminant is $-27$
C. There are two imaginary solutions.