Answer:
[tex]f(x)=5x^2+25x-30[/tex]
Step-by-step explanation:
Quadratic Equation
If the roots of a quadratic equation are known, we can form the equation as follows:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
where x1 and x2 are the known roots, and a is the leading coefficient.
We are given the roots as x1=1 and x2=-6, and the leading coefficient as a=5, thus:
[tex]f(x)=5(x-1)(x+6)[/tex]
Operating:
[tex]f(x)=5(x^2-x+6x-6)[/tex]
Simplifying:
[tex]f(x)=5(x^2+5x-6)[/tex]
Multiplying:
[tex]\mathbf{f(x)=5x^2+25x-30}[/tex]
