question 17 of 30 which of the following correctly describes the roots of the quadratic equation shown…

question 17 of 30 which of the following correctly describes the roots of the quadratic equation shown below? (x^{2}-6x + 12=0) a. 2 irrational roots b. 1 rational (double) root c. 2 rational roots d. 2 complex roots

question 17 of 30 which of the following correctly describes the roots of the quadratic equation shown below? (x^{2}-6x + 12=0) a. 2 irrational roots b. 1 rational (double) root c. 2 rational roots d. 2 complex roots

Answer

Explanation:

Step1: Recall the discriminant formula

For a quadratic equation $ax^{2}+bx + c = 0$, the discriminant $\Delta=b^{2}-4ac$. In the given equation $x^{2}-6x + 12=0$, we have $a = 1$, $b=-6$, and $c = 12$.

Step2: Calculate the discriminant

$\Delta=(-6)^{2}-4\times1\times12=36 - 48=-12$.

Step3: Determine the nature of the roots

If $\Delta>0$, the equation has two distinct real roots (rational if $\Delta$ is a perfect - square, irrational if $\Delta$ is not a perfect - square). If $\Delta = 0$, the equation has one rational double root. If $\Delta<0$, the equation has two complex roots. Since $\Delta=-12<0$, the equation $x^{2}-6x + 12=0$ has two complex roots.

Answer:

D. 2 complex roots