Question

question 2 of 10
which two values of x are roots of the polynomial below?
x² - 11x + 17
a. x = (11 + √(-109))/4
b. x = (11 + √53)/2
c. x = 2.5
d. x = (11 - √(-109))/4
e. x = (11 - √53)/2
f. x = 3

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the roots are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Here, \(a = 1\), \(b=-11\), \(c = 17\).

Step2: Calculate Discriminant

Discriminant \(D=b^2-4ac=(-11)^2-4\times1\times17=121 - 68 = 53\).

Step3: Apply Quadratic Formula

Substitute \(a\), \(b\), \(D\) into the formula:
\(x=\frac{-(-11)\pm\sqrt{53}}{2\times1}=\frac{11\pm\sqrt{53}}{2}\).

Answer:

B. \(x = \frac{11+\sqrt{53}}{2}\), E. \(x = \frac{11-\sqrt{53}}{2}\)