Check all of the numbers that are potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9.

Possible Roots are ±1, ±3 and ±9

Step-by-step explanation:

The roots of a polynomial (also called zeros of a polynomial) are the values ​​for which the numerical value of the polynomial equals zero.

Given a polynomial  

aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² +...+ a₂x² + a₁x +a₀

the possible roots of the polynomial are , where p are the factors of a₀ (the Trailing Constant) and q are the factors of aₙ (the Leading Coefficient)

In the case of the polynomial:

f(x) = x⁴ – 2x³ + 5x² – 7x + 9

The Leading Coefficient is aₙ=1  and the Trailing Constant is  a₀=9.

The factors are:

So, Possible Roots are ±1, ±3 and ±9

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x