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Question

For #29-31, write a polynomial function f of least degree that has a leading coefficient of 1 and

the given zeros.

29. - 4, - 2,5

30. 4,6 - √7

31. 0,5, - 5 +√8

Answer 1

-4,-2,5 zeros

x=-4, x+4=0

x=-2, x+2=0

x=5, x-5=0

have factors (x+4)(x+2)(x-5)

f(x) = (x^2+6x+8)(x-5)

= x^3 +x^2 -22x -40

x=4, x-4=0

x=6-sqr7, x-6=-sqr7, x^2-12x+36 = 7

have factors (x-4)(x^2-12x+29)

f(x)=x^3 -16x^2 +77x -116

x=0, x=5, x=-5+sqr8

have factors x, x-5 and x^2 -10x+17

f(x) = x(x-5)(x^2-10x+17)

= x(x^3-15x^2+67x -86)

= x^4 -15x^3+57x^2-86x