Answer:
After factoring, to find the solutions of a quadratic equation, we have to apply the Zero Product rule by setting each of the factors to zero and solving for the variable.
The solutions of the given equation is x = 4 and x = -1
Explanation:
Given the below quadratic equation;
[tex]x^2-3x-4=0[/tex]
The first step to solving the above is to look for two factors of -4 whose sum will give -3. These numbers are -4 and 1. So let's go ahead and replace the middle term with these two factors as shown below;
[tex]x^2-4x+x-4=0[/tex]
The 2nd step is to factorize;
[tex]\begin{gathered} x(x-4)+(x-4)=0_{} \\ (x-4)(x+1)=0 \end{gathered}[/tex]
The 3rd step is to apply the Zero Product Rule, by setting each factor to zero and solving for x;
[tex]\begin{gathered} x-4=0 \\ x=4 \\ or \\ x+1=0 \\ x=-1 \end{gathered}[/tex]
