Question

show what you know quadratic formu
solve: $2n^2 - n - 6 = 0$
$\square -\frac{3}{2}$
$\square -2$
$\square \frac{3}{2}$
$\square 2$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(2n^2 - n - 6 = 0\). We look for two numbers that multiply to \(2\times(-6)= -12\) and add up to \(-1\). The numbers are \(-4\) and \(3\).
So we rewrite the middle term:
\(2n^2 - 4n + 3n - 6 = 0\)
Factor by grouping:
\(2n(n - 2) + 3(n - 2) = 0\)
\((2n + 3)(n - 2) = 0\)

Step2: Solve for \(n\)

Set each factor equal to zero:

• For \(2n + 3 = 0\), we have \(2n = -3\), so \(n = -\frac{3}{2}\)
• For \(n - 2 = 0\), we have \(n = 2\)

Answer:

The solutions are \(n = -\frac{3}{2}\) and \(n = 2\), so the correct options are \(-\frac{3}{2}\) (A. \(-\frac{3}{2}\)) and \(2\) (D. \(2\))