f(x)=x4(6-8x9)
(1) Roots are found by solving x4(6-8x9)=0, so x4=0⇒x=0 is a root.
6-8x9=0⇒3-4x9=0⇒3=4x9, x9=¾, x=9√¾=0.96854 approx. is another root.
There are just two real roots.
(2) As x→∞, f(x)→-∞ because 6-8x9 is a negative number when x is large and positive, while x4 is always positive, making the product large negative.
(3) As x→-∞, f(x)→∞ because x9 is negative (odd exponent), so 6-8x9 is large and positive. The product is therefore large positive.