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

Sagot :

Answer:

[tex]f(x)=x^3-7x^2-6x+72[/tex]

Step-by-step explanation:

[tex]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[/tex]

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