Is 3/5 A Zero of f(x)?

[harpazo]

Is 3/5 a zero of f(x) = 2x^6 - 5x^4 + x^3 - x + 1?

Let me guess. I replace each x in f(x) with 3/5. If the result is f(0) = 0, then the answer to the question is yes. Correct?

 

[Deleted member 4993]

Is 3/5 a zero of f(x) = 2x^6 - 5x^4 + x^3 - x + 1?

Let me guess. I replace each x in f(x) with 3/5. If the result is f(0) = 0, then the answer to the question is yes. Correct?

Correct.

However, there is a theorem called "rational root theorem" which will indicate that 3/5 is not a root of the given polynomial with observation only.

 

[harpazo]

Correct.

However, there is a theorem called "rational root theorem" which will indicate that 3/5 is not a root of the given polynomial with observation only.

Does 2x^6 - 5x^4 + x^3 - x + 1 = 0 when x = 3/5?

2(3/5)^6 - 5(3/5)^4 + (3/5)^3 - (3/5) + 1 = 0?

928/15625 = 0?

I now know that 3/5 is not a zero of the given polynomial function.

 

[MarkFL]

Does 2x^6 - 5x^4 + x^3 - x + 1 = 0 when x = 3/5?

2(3/5)^6 - 5(3/5)^4 + (3/5)^3 - (3/5) + 1 = 0?

928/15625 = 0?

I now know that 3/5 is not a zero of the given polynomial function.

The rational roots theorem tells us that if the given polynomial has any rational roots, they must be from the list:

[MATH]x=\pm\frac{1}{2},\pm1[/MATH]
Because 3/5 is not included, we then know it cannot be a rational root.