SOLUTION: Find a possible formula for a polynomial f that has degree 2 or less, f(1)=f(4)=0 and f(2)=6.
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Question 1188485: Find a possible formula for a polynomial f that has degree 2 or less, f(1)=f(4)=0 and f(2)=6.
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
formula for a polynomial f that has degree 2 is
given:
and
these are points
(,)
(,)
(,)
use them to find ,, and
............solve for
..........eq.1
............solve for
.........eq.2
............solve for
.........eq.3
from eq.1 and eq.2 we have
........solve for
..........eq. 1a
from eq.1 and eq.3 we have
......solve for
............eq.1b
from eq.1a and eq.1b we have
......solve for
substitute in eq. 1a
substitute and in eq. 1
..........eq.1
so,
, ,
and your equation is
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
The solution from the other tutor is algebraically correct; but it is very inefficient.
Given that there are two roots at x=1 and x=4, and that the degree is to be 2 or less, we know that in fact it is degree 2.
And given those two roots, we know the polynomial is of the form
To finish finding the polynomial, us the given information that f(2)=6:
ANSWER:
One form of the polynomial function is
In standard polynomial form that is
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.
May Lord save you from solving this problem in a way as @MathLover1 does it . . .
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