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f() is a three degree polynomial such that f(1) =1, f(2) =2, f(3)= 3, f(4) =12 then find f(0) = ?

f() is a three degree polynomial such that f(1) =1, f(2) =2, f(3)= 3, f(4) =12 then find f(0) = ?

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2 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
let the polynomial be ax3 +bx2 + cx + d .  Then f(0) = d.  
To find the value of d,  solve the equations
f(1) = a + b + c + d =1
f(2) = 8a + 4b + 2c + d = 2
f(3) = 27a + 9b + 3c + d = 3
f(4) = 64a + 16b + 4c + d = 12
KAPIL MANDAL
132 Points
9 years ago
By solving above equations, you can get a,b,c,d. But, be clever. x2, x3, x  will be zero for f(0). So, you have to calculate only d as said by RAJYALAXMI. I cannot find the way to write matrices here. Sorry for that. Solving by cramer’s rule, d = -8. 

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