SOLUTION: Let f( x)be fourth degree polynomial with coefficient of x4 is 1 such that f(-1)=-1;f(2)=-4; f(-3)=-9 and f(4)=-16 than that value of f(1) is

Algebra ->  Functions -> SOLUTION: Let f( x)be fourth degree polynomial with coefficient of x4 is 1 such that f(-1)=-1;f(2)=-4; f(-3)=-9 and f(4)=-16 than that value of f(1) is       Log On


   

Question 984303: Let f( x)be fourth degree polynomial with coefficient of x4 is 1 such that f(-1)=-1;f(2)=-4;
f(-3)=-9 and f(4)=-16 than that value of f(1) is
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E4%2Bax%5E3%2Bbx%5E2%2Bcx%2Bd
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f%28-1%29=1-a%2Bb-c%2Bd=-1
1.-a%2Bb-c%2Bd=-2
.
.
f%282%29=16%2B8a%2B4b%2B2c%2Bd=-4
2.8a%2B4b%2B2c%2Bd=-20
.
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f%28-3%29=81-27a%2B9b-3c%2Bd=-9
3.-27a%2B9b-3c%2Bd=-90
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f%284%29=256%2B64a%2B16b%2B4c%2Bd=-16
4.64a%2B16b%2B4c%2Bd=-272
.
.
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Using Cramer's method,
a=-2
b=-14
c=14
d=24
So,
f%281%29=1%5E4-2%281%29%5E3-14%281%29%5E2%2B14%281%29%2B24
f%281%29=1-2-14%2B14%2B24
f%281%29=23