SOLUTION: FIND THE POLYNOMIAL f(x) OF DEGREE THREE THAT HAS ZEROES AT 1,2, AND 4 SUCH THAT f(0)=-16.

Question 62976: FIND THE POLYNOMIAL f(x) OF DEGREE THREE THAT HAS ZEROES AT 1,2, AND 4 SUCH THAT f(0)=-16.
Found 2 solutions by uma, Nate:
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Given that the polynomial has zeroes at 1, 2 and 4.
So the required polynomial will be :
a(x-1)(x-2)(x-4)
==> a(x-1)(x^2 - 2x - 4x + 8)
= a(x-1)(x^2 - 6x + 8)
= ax^3 - 6ax^2 + 8ax - ax^2 + 6ax - 8a
= ax^3 - 7ax^2 + 14ax - 8a
f(0) = - 8a
==> - 8a = - 16
==> a = 2
Thus f(x) = 2x^3 - 14x^2 + 28x - 16
is the required polynomial.
Good Luck!!!

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
(x - 1)(x - 2)(x - 4)
(x^2 - 3x + 2)(x - 4)
x^3 - 3x^2 + 2x - 4x^2 + 12x - 8
x^3 -7x^2 + 14x - 8 = f(x)

All values for x is zero ... so f(0) = - 8
2*f(0) = -16
2x^3 - 14x^2 + 28x - 16 = f(x)

RELATED QUESTIONS
Find the polynomial f(x) of degree three that zeroes at 1, 2, and 4 such that f(0)=-16. (answered by adamchapman,Nate)
PLEASE HELP ME WITH THIS PROBLEM: Find the polynominal f(X) of degree three that has... (answered by Edwin McCravy)
Find the polynomial f(x) of degree three that has zeroes at 1,2, and 4 such that... (answered by AnlytcPhil)
find the polynomial f(x) of degree three that has zeroes at 1,2 and 4 such that... (answered by AnlytcPhil)
Find the polynomial f(x)of degree three that has zeroes at 1,2 and 4 such that f(0)=-16. (answered by Nate)
Find the polynmial f(x) of degree three that has zeroes at 1, 2 and 4 such that f(0)=-16. (answered by rapaljer)
someone please show or explain the easiest way to understand this Find the polynomial... (answered by stanbon)
Find the polynomial f(x) of degree three that has zeroes at 1, 2 and 4 such that... (answered by Edwin McCravy,stanbon)
Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given... (answered by greenestamps)
Find a polynomial f(x), that has the degree of 4 or less, so f(−2) = 0,... (answered by ikleyn)