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

Answer:

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

Step-by-step 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 $x-4=0$.