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Chapter 4: Q. 4 (page 247)

Solve $3 x^{3} + 2 x - 1 = 8 x^{2} - 4$ in the complex number system.

Short Answer

Expert verified

The given function is not a polynomial function.

Step by step solution

01

Step 1. Given Information

The given function is $3 x^{3} + 2 x - 1 = 8 x^{2} - 4$

02

Step 2. Explanation

The function $f (x) = 3 x^{2} + 5 x^{\frac{1}{2}} - 1$ is not in the form of a polynomial function because the power of role="math" localid="1646298448381" $x, \frac{1}{2}$ is not an integer.

Thus, the given function is not a polynomial function.

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Most popular questions from this chapter

Use the Factor Theorem to prove that $x - c$ is a factor of

$x^{n} - c^{n}$ for any positive integer n.

Find the real zeros of f. Use the real zeros to factor f.

$f (x) = 4 x^{4} - 15 x^{3} - 8 x^{2} + 15 x + 4$

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = x^{5} - x^{4} + 2 x^{2} + 3$

In Problems 39–56, find the real zeros of f. Use the real zeros to factor f.

$f (x) = 4 x^{4} + 7 x^{2} - 2$

In Problems 39–56, find the real zeros of f. Use the real zeros to factor f.

$f (x) = 2 x^{4} + 11 x^{3} - 5 x^{2} - 43 x + 35$

See all solutions

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