Question

solve for v.
$v^2 - v - 6 = 0$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$v = \square$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(v^2 - v - 6 = 0\). We look for two numbers that multiply to \(-6\) and add up to \(-1\). The numbers are \(-3\) and \(2\) because \((-3)\times2=-6\) and \(-3 + 2=-1\). So we can factor the equation as \((v - 3)(v + 2)=0\).

Step2: Solve for \(v\) using zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((v - 3)(v + 2)=0\), we set each factor equal to zero:

• If \(v - 3=0\), then \(v=3\) (by adding 3 to both sides of the equation \(v - 3 = 0\)).
• If \(v + 2=0\), then \(v=-2\) (by subtracting 2 from both sides of the equation \(v + 2 = 0\)).

Answer:

\(3,-2\)