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Which statement about the polynomial function g(x) is true?

1If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

2If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

3If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

4If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

Respuesta :

When leading coefficient is 1 , the root will be an integer for g(x) = 0

Option 4 is the right answer.

What is a Polynomial Function ?

Functions of independent variable in which the variable can appear more than once with different powers.

[tex]\rm g(x) = a_n x^n + a_{n-1}x^{n-1} + ................+ a_o[/tex]

Let this represents the polynomial function

where [tex]\rm a_n \; is\;the \;leading \; coefficient \; a_o \; is \;the\;last \;term[/tex]

Then the according to rational root theorem ,

The root of the function is given by

[tex]\rm \dfrac{p}{q} = \dfrac{factor \;of\; the\; last\; term}{factor \;of \;the\; leading coefficient}[/tex]

So when leading coefficient is 1 , the root will be an integer for g(x) = 0

Option 4 is the right answer.

To know more about Polynomial function

https://brainly.com/question/12976257

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