find all zeros of the function

Question

6x^3+43x^2+6x+7

Answer 1

clearly you are intended to use the Rational Zeroes Theorem, and start guessing. A little synthetic division reveals that there are no rational roots at all.

So, the only possible roots will involve cube roots, and be very hard to find.

I suggest graphing it and approximating the value(s)

Since all the coefficients are positive, Descartes' Rule of Signs says that there are no positive real roots.

So, look for a negative root. Wolframalpha.com says it's at about -7.05