Question

Does `f(x) = x^7+2x^6+3x^5+4x^4+5x^3+6x^2+7x+8` have at least one real root?

Answer 1

Yes

Explanation:

Any polynomial function of odd degree with real coefficients has at least one real zero, by the intermediate value theorem.

Given:

`f(x) = x^7+2x^6+3x^5+4x^4+5x^3+6x^2+7x+8`

We find:

`f(-2) = -128+128-96+64-40+24-14+8 = -54`

`f(0) = 8`

So `f(x)` has some zero in `(-2, 0)`