Question

Use the intermediate value theorem to determine whether the polynomial function has a real zeros between the given integers.

Answer 1

$f(1)=-5\cdot1^4+8\cdot1^3+6\cdot1+1=-5+8+6+1=10\\ f(2)=-5\cdot2^4+8\cdot2^3+6\cdot2+1=-80+64+12+1=-3\\\\ f(1)>0\\ f(2)$
It does.