Question

final review
score: 42/100 answered: 9/17
question 10
solve ( x^2 + 11x + 15 = 0 ) by using the quadratic formula.
the solution set is { }.
hint: reduce fractions. express answers as two numbers separated by a comma. no decimal approximations.

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 1\), \(b = 11\), \(c = 15\).

Step2: Calculate Discriminant

First, find the discriminant \(D=b^2 - 4ac\). Substitute \(a = 1\), \(b = 11\), \(c = 15\):
\(D=(11)^2-4(1)(15)=121 - 60 = 61\).

Step3: Apply Quadratic Formula

Substitute \(a = 1\), \(b = 11\), \(D = 61\) into the formula:
\(x=\frac{-11\pm\sqrt{61}}{2(1)}=\frac{-11\pm\sqrt{61}}{2}\).

Answer:

\(\frac{-11 + \sqrt{61}}{2},\frac{-11 - \sqrt{61}}{2}\)