Question
Find a polynomial of the specified degree that satisfies the given conditions.
Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4
Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4
Answers
zeros −3, 0, 1, 4 -->x(x+3)(x-1)(x-4)
expanding this gives us
x^4 - 2x^3 - 11x^2 + 12x
but we are told that the x^3 terms is 4x^3
and we have it as -2x^3
so there had to be a -2 in front of the whole mess
polynomial is -2x(x-1)(x-4)(x+3)
or
-2x^4 + 4x^3 + 22x^2 - 24x
expanding this gives us
x^4 - 2x^3 - 11x^2 + 12x
but we are told that the x^3 terms is 4x^3
and we have it as -2x^3
so there had to be a -2 in front of the whole mess
polynomial is -2x(x-1)(x-4)(x+3)
or
-2x^4 + 4x^3 + 22x^2 - 24x
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