Solve 6m2 - m − 2 = 0 using the quadratic formula.

Question

ScanSolve AI Tutor · Accepted Answer

Let's solve question 9 using the quadratic formula.

The equation is $6m^2 - m - 2 = 0$ .

Identify the coefficients $a$ , $b$ , and $c$ .
Comparing $6m^2 - m - 2 = 0$ with the standard quadratic form $am^2 + bm + c = 0$ , we have:
$a = 6$
$b = -1$
$c = -2$
Apply the quadratic formula.
The quadratic formula is $m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute the values of $a$ , $b$ , and $c$ into the formula.
$m = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(6)(-2)}}{2(6)}$
Simplify the expression.
$m = \frac{1 \pm \sqrt{1 - (-48)}}{12}$ $m = \frac{1 \pm \sqrt{1 + 48}}{12}$ $m = \frac{1 \pm \sqrt{49}}{12}$ $m = \frac{1 \pm 7}{12}$
Calculate the two possible solutions for $m$ .
For the positive root:
$m_1 = \frac{1 + 7}{12} = \frac{8}{12} = \frac{2}{3}$
For the negative root:
$m_2 = \frac{1 - 7}{12} = \frac{-6}{12} = -\frac{1}{2}$
The solutions are $m = \frac{2}{3}$ and $m = -\frac{1}{2}$ .
$m = \frac{2}{3}, -\frac{1}{2}$

Solve 6m2 − m − 2 = 0 using the quadratic formula.