Question

compute the discriminant. then determine the number and type of solutions of the given equation.\\(3x^2 - 3x + 3 = 0\\)\\(\dots\\)what is the discriminant?\\(\square\\) (simplify your answer.)

Explanation:

Step1: Recall discriminant formula

For quadratic $ax^2+bx+c=0$, discriminant $D=b^2-4ac$

Step2: Identify coefficients

$a=3$, $b=-3$, $c=3$

Step3: Calculate discriminant

$D=(-3)^2-4(3)(3)=9-36$

Step4: Simplify the result

$D=-27$

Step5: Analyze solution type

Negative $D$ means 2 complex solutions.

Answer:

The discriminant is $\boldsymbol{-27}$. The equation has 2 distinct non-real (complex) solutions.