102k views
12 votes
write a polynomial fuction f of least degree that has rational coefficients, a leading coefficient of 1, and the zeroes of 6,-3, & 4.​

1 Answer

10 votes

Answer:


f(x)=x^3-7x^2-6x+72

Explanation:


f(x)=a(x-p)(x-q)(x-r)\\\\f(x)=1(x-6)(x+3)(x-4)\\\\f(x)=(x^2-3x-18)(x-4)\\\\f(x)=x^3-4x^2-3x^2+12x-18x+72\\\\f(x)=x^3-7x^2-6x+72

This is because
x=6 is the solution to
x-6=0,
x=-3 is the solution to
x+3=0, and
x=4 is the solution to
x-4=0.

User Hjuster
by
6.8k points