Question

1. $x^2 + 7x + 12 = 0$

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(12\) (the constant term) and add up to \(7\) (the coefficient of \(x\)). The numbers \(3\) and \(4\) satisfy this, since \(3\times4 = 12\) and \(3 + 4=7\). So we can factor the quadratic as:
\(x^{2}+7x + 12=(x + 3)(x + 4)\)
So the equation becomes \((x + 3)(x + 4)=0\)

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

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For \((x + 3)(x + 4)=0\), we set each factor equal to zero:

• If \(x+3 = 0\), then \(x=-3\)
• If \(x + 4=0\), then \(x=-4\)

Answer:

The solutions of the equation \(x^{2}+7x + 12 = 0\) are \(x=-3\) and \(x=-4\)