Question

The polynomial equation x^4+x^3+x^2+x+1
Has zero positive real roots. True or false

Answer 1

Answer:

True. that polynomial has NO real roots, positive or otherwise.

Step-by-step explanation:

stare at it carefully. you should have seen that thing when you first learned about factoring polynomials. If not, I'll spoil the fun for you and nudge you in the right direction by multiplying it by

$(1 - x)$

a lots of terms will cancel out, and you will be left with

$1 - {x}^{5}$

At this point we're looking at a different problem: how many real numbers, elevated to the first power, are equal to 1? the answer is: only one real number, 1 itself. problem is, we introduced it ourselves, so the part we started with will give us more roots - none of them real numbers.