Question

What is a 3rd degree polynomial function like f(0)=18 and whose zeros are -1, 2 ,and 3

Answer 1

Your polynomial has the form:
\[y=ax ^{3}+bx ^{2}+cx+d\]
For f(0)=18 : your x=0 and y=18
\[y=a*0 ^{3}+b*0 ^{2}+c*0+d\]
D=18
And the zeros are when your y=0
so , you have
for x=-1
\[0=-a+b-c+d\]
\[0=-a+b-c+18\]
for x=2
\[0=8a+4b+2c+d\]
\[0=8a+4b+2c+18\]
for x=3
\[0=27a+9b+3c+d\]
\[0=27a+9b+3c+18\]
You need to solve this system of 3 equations to find a,b and c

Answer 2

you can do it with matrices or by elimination

Answer 3

thanks so much!!

Answer 4

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Happy OpenStudying!

Answer 5

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Answer 6

Try this:\[f(x) = k(x+1)(x-2)(x-3)\]\[f(0) = k\cdot1 \cdot (-2) \cdot (-3) = 6k = 18 \Rightarrow k = 3\]So\[f(x) = 3(x+1)(x-2)(x-3)\]