Question

Use the quadratic formula to solve the quadratic equation 2x²9x+11= 0.

Express its solutions in the form a±bi

Answer 1

To solve the quadratic equation \(2x^2 + 9x + 11 = 0\) using the quadratic formula, we start by identifying the coefficients:

- \(a = 2\)
- \(b = 9\)
- \(c = 11\)

The quadratic formula is given by:

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

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

\[
b^2 - 4ac = 9^2 - 4 \cdot 2 \cdot 11 = 81 - 88 = -7
\]

Since the discriminant is negative, the solutions will be complex. Now we can substitute the values into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{-7}}{2 \cdot 2} = \frac{-9 \pm \sqrt{7}i}{4}
\]

So the solutions in the form \(a \pm bi\) are:

\[
x = -\frac{9}{4} \pm \frac{\sqrt{7}}{4}i
\]

Thus, the final answers are:

\[
x = -\frac{9}{4} + \frac{\sqrt{7}}{4}i \quad \text{and} \quad x = -\frac{9}{4} - \frac{\sqrt{7}}{4}i
\]