Question

what are all the solutions of $x^2 + 3x - 4 = 0$?
□ -4
□ -2
□ -1
□ 0
□ 1
□ 2
□ 4
done

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^{2}+3x - 4 = 0\). We look for two numbers that multiply to \(- 4\) and add up to \(3\). The numbers are \(4\) and \(-1\) since \(4\times(-1)=-4\) and \(4+( - 1)=3\). So we can factor the equation as \((x + 4)(x-1)=0\)

Step2: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((x + 4)(x - 1)=0\), we set each factor equal to zero:

• When \(x+4=0\), we solve for \(x\) by subtracting \(4\) from both sides: \(x=-4\)
• When \(x - 1=0\), we solve for \(x\) by adding \(1\) to both sides: \(x = 1\)

Answer:

\(-4\), \(1\)