Question

question 4 of 10
which two values of x are roots of the polynomial below?
x² + 5x + 7
a. x = (5 - √17)/2
b. x = 1/2
c. x = (-5 + √-3)/2
d. x = (-5 - √-3)/2
e. x = (5 + √17)/2
f. x = 5

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, \(a = 1\), \(b = 5\), \(c = 7\).

Step2: Calculate Discriminant

Discriminant \(D=b^2-4ac=(5)^2 - 4\times1\times7=25 - 28=- 3\).

Step3: Find Roots

Substitute \(a\), \(b\), and \(D\) into the quadratic formula: \(x=\frac{-5\pm\sqrt{-3}}{2}\). So the two roots are \(x=\frac{-5 + \sqrt{-3}}{2}\) and \(x=\frac{-5-\sqrt{-3}}{2}\).

Answer:

C. \(x = \frac{-5+\sqrt{-3}}{2}\), D. \(x=\frac{-5-\sqrt{-3}}{2}\)