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

1. anonymous

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

2. anonymous

you can do it with matrices or by elimination

3. anonymous

thanks so much!!

4. anonymous

Try tipping those you help you out by pressing on that "Best Response" button to reward them a medal. Happy OpenStudying!

5. anonymous

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6. ParthKohli

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)$