Question

Find the zeros x^4-2x^3-44x^2-88x-32

Answer 1

The zeros which are the roots of the polynomial expressions are:

x = -4; x = - 2;  x = 4 - 2√5;  x = 2(2 + √5)

What are the zeros of a polynomial expression?

The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.

For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.

From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:

Using the rational root theorem:

$\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }$

$\mathbf{=(x+2) (x^3-4x^2-36x-32) }$

By factorization, we have:

= (x + 2) (x + 4) (x² - 8x - 4)

The zeros which are the roots of the polynomial expressions are:

x = -4; x = - 2;  x = 4 - 2√5;  x = 2(2 + √5)

Learn more about zeros of polynomial here:

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