Find a polynomial f(x) of degree 3 that has the

Arthur Pratt 2021-12-15 Answered
Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.
−5, 2, 1; f(3) = 64
f(x) =
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Expert Answer

veiga34
Answered 2021-12-16 Author has 32 answers
Step 1
here we use the linear factors for the zeroes given
see below the calculation
Step 2
Given zeros are −5,2,1
then the linear factor that divide the polynomial f(x) are (x+5),
(x-2),(x-1)
then f(x)=m(x+5)(x-2)(x-1) but to satisfy the another conditions that f(3)=64
we see that f(3)=m(3+5)(3-2)(3-1)=12m
then 12m=64 we get m=163
then required 3 degree polynomial is f(x)=163(x+5)(x2)(x1)
=163(x3+2x213x+10)
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Pansdorfp6
Answered 2021-12-17 Author has 27 answers
Given zeroes -5,2,1
Equation of polynomial
f(x)=k(x-(-5))(x-2)(x-1)
=k(x+5)(x-2)(x-1)
=k(x22x+5x10)(x1)
=k(x2+3x10)(x1)
=k(x3x2+3x23x10x+10)
=k(x3+2x213x+10)
f(x)=k(x3+2x213x+10)
Given f(3)=64
k(33+2x3213x3+10)=64
k(27+1839+10)=64
16k=64
k=64164
f(x)=4(x3+2x213x+10)
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