To solve the given quadratic equation and find the values of [tex]\( x \)[/tex], let's follow the steps below:
1. Starting with the quadratic equation:
[tex]\[
y = x^2 + 3x - 4
\][/tex]
2. We know that the quadratic equation can be factored into:
[tex]\[
y = (x + 4)(x - 1)
\][/tex]
3. To find the roots of the equation, we set [tex]\( y = 0 \)[/tex]:
[tex]\[
0 = (x + 4)(x - 1)
\][/tex]
4. Setting each factor equal to zero gives us two equations to solve:
- [tex]\( x + 4 = 0 \)[/tex]
- [tex]\( x - 1 = 0 \)[/tex]
5. Solving the first equation [tex]\( x + 4 = 0 \)[/tex]:
[tex]\[
x + 4 = 0 \implies x = -4
\][/tex]
6. Solving the second equation [tex]\( x - 1 = 0 \)[/tex]:
[tex]\[
x - 1 = 0 \implies x = 1
\][/tex]
7. Thus, the solutions for [tex]\( x \)[/tex] are:
[tex]\[
x = -4 \quad \text{and} \quad x = 1
\][/tex]
So, the correct values of [tex]\( x \)[/tex] that satisfy the equation are [tex]\( -4 \)[/tex] and [tex]\( 1 \)[/tex].
To summarize, the roots of the quadratic equation [tex]\( y = x^2 + 3x - 4 \)[/tex] are [tex]\( x = -4 \)[/tex] and [tex]\( x = 1 \)[/tex].
