Answer:
Option A - (x + 1) and (x – 4)
Step-by-step explanation:
Given : The trinomial [tex]x^2-3x-4[/tex] is represented by the model.
To find : What are the factors of the trinomial?
Solution : The given trinomial is a quadratic equation [tex]y=ax^2+bx+c[/tex]
so we solve using by discriminant method.
Solution of x is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Comparing with given quadratic equation [tex]y=x^2-3x-4[/tex]
where a=1, b=-3, c=-4
Solution is given by
[tex]x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}[/tex]
[tex]x=\frac{3\pm\sqrt{9+16}}{2}[/tex]
[tex]x=\frac{3\pm\sqrt{25}}{2}[/tex]
[tex]x=\frac{3\pm5}{2}[/tex]
[tex]x=\frac{3+5}{2},\frac{3-5}{2}[/tex]
[tex]x=4,-1[/tex]
The factors are (x-4),(x+1)
Therefore, Option A is correct.
The factors of trinomial [tex]x^2-3x-4=(x-4)(x+1)[/tex]
