Question

Select the two values of x that are roots of this equation.
2x2 + 11x +15=0
•x=-6
0 x=-3
0 x=-5
0 x = -5/2

Answer 1

To find the roots of the quadratic equation \(2x^2 + 11x + 15 = 0\), we can use the quadratic formula:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]

In this case, \(a = 2\), \(b = 11\), and \(c = 15\).

First, we calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = 11^2 - 4 \cdot 2 \cdot 15 = 121 - 120 = 1
\]

Now, we can plug \(b\) and the discriminant back into the quadratic formula:

\[
x = \frac{{-11 \pm \sqrt{1}}}{2 \cdot 2}
\]

This simplifies to:

\[
x = \frac{{-11 \pm 1}}{4}
\]

Now we calculate the two possible values for \(x\):

1. Using the positive square root:
\[
x = \frac{{-11 + 1}}{4} = \frac{{-10}}{4} = -\frac{5}{2}
\]

2. Using the negative square root:
\[
x = \frac{{-11 - 1}}{4} = \frac{{-12}}{4} = -3
\]

Thus, the roots of the equation \(2x^2 + 11x + 15 = 0\) are:

- \(x = -3\)
- \(x = -\frac{5}{2}\)

So the correct values from the given options are:

- \( x = -3 \)
- \( x = -\frac{5}{2} \)