Question

According to The Fundamental Theorem of Algebra, how many zeros does the function f(x) = 24x5 + 8x3 - 2x - 15 have?

Answer 1

USE DISCRIMANT

Answer 2

You need to check the highest power of the X, then how many factors like (x-a), (x-b) are required to raise x to that power.

Answer 3

@Juanita, No, that's wrong.

The Fundamental Theorem of Algebra says that a polynomial of order n has n roots.

Hence to apply the FTA to this problem, you need to know the order of this polynomial.

Answer 4

The order of a polynomial, as mainaknag says, is the highest order of the variable.

Answer 5

yes correct there are n zeores, the roots can be real or imaginary

Answer 6

So Skate, what's the highest power of x in this polynomial?
\[ f(x) = 24x^5 + 8x^3 - 2x - 15 \]

Answer 7

i have no idea sorry

Answer 8

24?

Answer 9

What is the highest power of x? 24 is coefficient

Answer 10

POWEr are exponents. so highest powere is 5

Answer 11

\( x \) is x to the power of 1. \( x^2 \) is x to the power of two. Hence a polynomial
\[ p(x) = 5x \] is of order 1.

A polynomial \[ q(x) = 3x^2 - 7 \] is of order 2.

Answer 12

So can you see now what is the highest power of x in your polynomial? Juanita just told you the answer.

Answer 13

yes

Answer 14

The highest power of x in
\[ f(x) = 24x^5 + 8x^3 - 2x - 15 \]
is \( x^5 \). Hence the polynomial is of fifth order. Hence by the FTA, it has ____ roots?

Answer 15

The Fundamental Theorem of Algebra says that a polynomial of order n has n roots.

Answer 16

5?

Answer 17

or 4

Answer 18

x^5 is the highest power
==> polynomial is of order 5
==> polynomial has 5 roots, by the Fundamental Theorem of Algebra.

Answer 19

Make sense?

Answer 20

yes thank you