Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
which answer shows the conjugate pair solutions to the equation $-5x^2 - 8 = -12x$? (1 point)
\\(\bigcirc\\) $-12 \pm 4i$
\\(\bigcirc\\) $\frac{6}{5} \pm \frac{2i}{5}$
\\(\bigcirc\\) $-\frac{6}{5} \pm \frac{2i}{5}$
\\(\bigcirc\\) $-12 \pm \frac{2i}{5}$

Explanation:

Step1: Rewrite the equation in standard form

First, we rewrite the given equation \(-5x^{2}-8 = -12x\) into the standard quadratic form \(ax^{2}+bx + c=0\).
Add \(12x\) to both sides and rearrange the terms:
\(-5x^{2}+12x - 8=0\)
Multiply both sides by \(- 1\) to make the coefficient of \(x^{2}\) positive:
\(5x^{2}-12x + 8 = 0\)
Here, \(a = 5\), \(b=-12\), \(c = 8\).

Step2: Use the quadratic formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).
First, calculate the discriminant \(\Delta=b^{2}-4ac\).
Substitute \(a = 5\), \(b=-12\), \(c = 8\) into the discriminant formula:
\(\Delta=(-12)^{2}-4\times5\times8=144 - 160=- 16\)
Since the discriminant is negative, the solutions will be complex numbers.
Now, substitute \(a = 5\), \(b = - 12\), and \(\Delta=-16\) into the quadratic formula:
\(x=\frac{-(-12)\pm\sqrt{-16}}{2\times5}=\frac{12\pm4i}{10}\)
Simplify the fraction by dividing the numerator and denominator by \(2\):
\(x=\frac{6\pm2i}{5}=\frac{6}{5}\pm\frac{2i}{5}\)

Answer:

\(\boldsymbol{\frac{6}{5}\pm\frac{2i}{5}}\) (the second option)