Which of the numbers below are potential roots of the function P x )= x4 22x2 16x 12?

The numbers that are potential roots of the function P(x) = x⁴+22x²-16x-12 are ±6 , ±1 and  ±3 .

The Roots of the equation can be calculated by using the rational roots theorem , which is written as ,

the root x = ± (factors of the constant term)/(factors of leading coefficient).

the function is given as : P(x) = x⁴ + 22x² - 16x - 12

from the above function , we can write that the constant term is = -12 ;

the leading coefficient term is = 1 .

we can write the factors of -12 as ±1, ±2, ±3, ±4, ±6 and ±12 .

the factors of 1 are ±1 .

So , By Rational root theorem , the possible roots are ±1, ±2, ±3, ±4, ±6 and ±12 .

the choices given in the question are ±6 , ±1 , ±3 .

Therefore , the potential roots are (a) ±6  , (b) ±1  and  (c) ±3 .

The given question is incomplete , the complete question is

Which of the numbers below are potential roots of the function P(x)=x⁴+22x²-16x-12  ?

(a) ±6

(b) ±1

(c) ±3

(d) ±8

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