Suppose somebody writes down an equation for a 5th-degree polynomial function
in standard form and tells you that it has only one real zero (but not where it is).
They tell you that you are allowed to ask any two questions about the polynomial,
and once those two questions have been answered, you should do your best to
graph the polynomial.

Question 1 -

What is location of one real zero?

Answer --> At , x= f we have one real zero.

Question 2 -

Whatis location of all other roots? Explain their nature ?

Explanation

Fifth order polynomial is of form :-

ax^5 + bx^4 + cx^3 + dx^2 + ex = 0

As it is one real zero , so it is of form:-

(x- f)( ax^4 + bx^3 + cx^2 + dx + e)

Question 1 -

What is location of one real zero?

Answer --> At , x= f we have one real zero.

Question 2 -

What is location of all other roots? Explain their nature ?

=>

Let us consider a 5th degree polynomial example.

1)

(x^5 -4x^4 + 3x^3 + 2x^2 + x+1 =0)

Has one real root at x = -0.577

​​​​2)

(x^5 − 4x^4 + 6x^3 − 4x^2 + x = 0)

Has one real root at x= 0

1) graph

2) graph

Step-by-step explanation:

right

step-by-step explanation:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2