highskye1
contestada

Pls help......
Which polynomial functions have only the roots 1 and 6? Check all that apply.
A) f(x) = (x – 1)(x – 6)
B) f(x) = 3(x + 1)(x + 6)
C) f(x) =(3x – 1)(x – 6)
D) f(x) = 3(x – 1)(x – 6)
E) f(x) = 6(x – 1)(x – 6)

Respuesta :

paulmchristman
If the two equations in parenthesizes were there own equations which ones would equal 1 and 6
(x-1) or x=1
(3x-1) or x=1/3
3(x-1) or 3x-3 or x=1
Do you understand?
MrRoyal

The roots of a polynomial are the zeros of the polynomial.

The functions have 1 and 6 as the roots are: (a) f(x) = (x – 1)(x – 6), (d) f(x) = 3(x – 1)(x – 6) and (e) 6(x – 1)(x – 6)

The roots are given as:

[tex]\mathbf{x = 1, x = 6}[/tex]

Equate to 0

[tex]\mathbf{x - 1 = 0, x - 6 = 0}[/tex]

Multiply the above expressions

[tex]\mathbf{(x - 1) \times (x -6) = 0 \times 0}[/tex]

[tex]\mathbf{(x - 1) \times (x -6) = 0 }[/tex]

Express as a function

[tex]\mathbf{f(x)= (x - 1) \times (x -6) }[/tex]

[tex]\mathbf{f(x)= (x - 1)(x -6) }[/tex]

As a general rule, we have:

[tex]\mathbf{f(x)=a (x - 1)(x -6) }[/tex]

Where:

[tex]\mathbf{a \ne 0}[/tex]

[tex]\mathbf{f(x)=a (x - 1)(x -6) }[/tex] represents all functions that have 1 and 6 as the roots.

So, options (a), (d) and (e) have 1 and 6 as the roots.

Read more about roots of polynomials at:

https://brainly.com/question/2770908

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