Question

show your work.

1. ( x^2 - 3x - 10 = 0 )

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(-10\) and add up to \(-3\). The numbers are \(-5\) and \(2\) since \((-5)\times2 = -10\) and \(-5 + 2=-3\). So we can factor the equation as:
\(x^{2}-3x - 10=(x - 5)(x + 2)=0\)

Step2: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).

• For \(x-5=0\), we get \(x = 5\).
• For \(x + 2=0\), we get \(x=-2\).

Answer:

\(x = 5\) or \(x=-2\)