Question

Which of the number(s) below are potential roots of the function? p(x) = x4 + 22x2 – 16x – 12 ±6 ±1 ±3 ±8

Answer 1

We are given Polynomial p(x) = x^4 + 22x^2 – 16x – 12.

We need to find the potential roots of the function.

We know, potential roots are all the rational numbers in terms of p/q.

Where p are the factors of constant term and q are the factors of leading coefficient.

For the given polynomial x^4 + 22x^2 – 16x – 12, we have constant term -12 and leading coefficent is the coefficent of x^4, that is 1.

So, the factors of -12 would be ±1,±2,±3,±4,±6 and ±12.

And factors of 1 is just ±1.

Therefore, ±1, ±2, ±3, ±4, ±6, ±12 would be it's potential roots.

In the given options, we can see ±6 ±1 ±3 are potential roots of the function.

Answer 2

Answer:

The potential roots of the function are ±6, ±1, ±3. The options 1, 2 and 3 are correct.

Step-by-step explanation:

The given function is

$p(x)=x^2+22x^2-16x-12$

According to the rational root theorem, all the possible roots of the function are in the form of

$x=\pm \frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}$

In the given function constant term is -12 and the leading coefficient is 1.

Factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12.

The factors of 1 are ±1.

By using rational root theorem, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore the options 1, 2 and 3 are correct.