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valkas [14]
3 years ago
9

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 10x^5 + 8x^4 - 15x^3 +2x^2 - 2

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Given:

The function is:

f(x)=10x^5+8x^4-15x^3+2x^2-2

To find:

All the possible rational zeros for the given function by using the Rational Zero Theorem.

Solution:

According to the rational root theorem, all the rational roots are of the form \dfrac{p}{q},q\neq 0, where p is a factor of constant term and q is a factor of leading coefficient.

We have,

f(x)=10x^5+8x^4-15x^3+2x^2-2

Here,

Constant term = -2

Leading coefficient = 10

Factors of -2 are ±1, ±2.

Factors of 10 are ±1, ±2, ±5, ±10.

Using the rational root theorem, all the possible rational roots are:

x=\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}.

Therefore, all the possible rational roots of the given function are \pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}.

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