Question

5.3 - online quiz - solving quadratic equations by fa
started: dec 12 at 6:18pm
quiz instructions
question 1
solve the following equation by factoring.
$x^2 + 7x + 12 = 0$
○ x = -4, x = -3
○ x = 4, x = 3
○ x = -4, x = 3
○ x = 4, x = -3

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^{2}+7x + 12\). We look for 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 because \(3\times4 = 12\) and \(3 + 4=7\). So, we can factor the quadratic as \((x + 3)(x + 4)=0\).

Step2: Solve for \(x\)

Using the zero - product property, if \((x + 3)(x + 4)=0\), then either \(x+3 = 0\) or \(x + 4=0\).

• For \(x+3 = 0\), subtracting \(3\) from both sides gives \(x=-3\).
• For \(x + 4=0\), subtracting \(4\) from both sides gives \(x=-4\).

Answer:

A. \(x=-4,x = - 3\)