Question

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

Answer 1

`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`.