Show that p(x) = 2x^3 − 5x^2 − 10x + 5 has a real root.

All odd degrees polynomials with real coefficients have (at least) a real root, and are continuous.  This is because the curve goes diagonally and must pass through the x-axis.

The above polynomial can be evaluated at x1=-10 and x1=+10 (or any other large enough number)
f(-10)=-2395
f(10)=1405
Since they have opposite signs, the function must intersect the x-axis between x1 and x2 by the intermediate value theorem, hence there is (at least) one root.

What are the following algebraic equations. you need to post those if you want the answer

Iwould say false, not positive but if prices went up for both stores, technically there will be less buyers?