Respuesta :
The other zeros of function m(x) = x^3 + 3x^2 - 2x - 4 are x = 2, x = -2
Zero of a function:
To find the zero of a function f(x), we need to find the value of f(0).
What is trinomial?
"A trinomial is a polynomial consisting of three terms."
For given question,
Given function : m(x) = x^(3) + 3x^(2) - 2x - 4
We need to find the zeros of a function.
to find the value of x for which m(x) = 0
x^(3) + 3x^(2) - 2x - 4 = 0
We know, x = -1 is a zero of given function.
So, (x + 1) is the factor of given trinomial x^(3) + 3x^(2) - 2x - 4 = 0.
To factorize above trinomial we divide it by x + 1.
Using synthetic division,
m(x)/(x + 1)
= (x^(3) + 3x^(2) - 2x - 4)/(x + 1)
= x^(2) + 2x - 4
So, x^(3) + 3x^(2) - 2x - 4 = (x + 1)(x^(2) + 2x - 4)
Now, to find other zeros of a function we solve the quadratic equation x^(2) + 2x - 4 = 0
⇒ x^(2) + 4x - 2x - 4 = 0
⇒ x(x + 2) - 2(x + 2) = 0
⇒ (x + 2)(x - 2) = 0
⇒ x + 2 = 0 or x - 2 = 0
⇒ x = -2 or x = 2
This means, x = -2 and x = 2 are other zeros of a function.
Learn more about zero of a function:
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