Respuesta :
Answer:
f(x) = x^3 - x^2 -2x
Step-by-step explanation:
If x = a is a zero of a polynomial, then x-a is a factor of the polynomial. Given the factors of a polynomial, the polynomial can be obtained by multiplying the factors.
The factors of the given polynomial are;
x - 2
x + 1
x
Multiplying the first two factors;
(x-2)(x+1) = x^2 + x -2x -2
= x^2 -x -2
We finally multiply this result by x to obtain our polynomial;
f(x) = x ( x^2 -x -2)
= x^3 - x^2 -2x
which is a cubic polynomial since it has 3 roots.
Answer:
f(x) = x³ - x² - 2x
Step-by-step explanation:
given a polynomial with zeros x = a, x = b, x = c
Then the factors are (x - a), (x - b) and (x - c)
and the polynomial is the product of the factors, that is
f(x) = k(x - a)(x - b)(x - c) ← where k is a multiplier
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Here the zeros are x = 2, x = - 1 and x = 0, thus the factors are
(x - 2), (x + 1) and (x - 0) , thus
y = kx(x - 2)(x + 1) ← let k = 1 and expand factors
= x(x² - x - 2) = x³ - x² - 2x
Hence a possible polynomial is
f(x) = x³ - x² - 2x
