Question

question
what are the roots of the equation $9x^2 + 36x + 40 = 0$ in simplest $a + bi$ form?

answer attempt 1 out of 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, \(a = 9\), \(b = 36\), \(c = 40\).

Step2: Calculate Discriminant (\(D=b^{2}-4ac\))

Substitute values: \(D=(36)^{2}-4\times9\times40\)
\(D = 1296-1440=-144\)

Step3: Find Roots Using Formula

\(x=\frac{-36\pm\sqrt{-144}}{2\times9}=\frac{-36\pm12i}{18}\)
Simplify: \(x=\frac{-36}{18}\pm\frac{12i}{18}=-2\pm\frac{2}{3}i\)

Answer:

The roots are \(-2+\frac{2}{3}i\) and \(-2-\frac{2}{3}i\)