Question

Consider the equation ^5 − 3^4 + ^3 + ^2 + + = 0 , where , , , ∈ .The equation has three distinct real roots which can be written as log2 a, log2 b and log2 c . The equation also has two imaginary roots, one of which is where d ∈ R.
(a) Show that a b c = 8 . The values a, b, and c are consecutive terms in a geometric sequence.
(b) Show that one of the real roots is equal to 1. (c) Given that q = 8d 2 , find the other two real roots.

Answer 1

Answer:

We can see from our sketch that as long as the turning point lies below the x-axis, the curve will meet the x-axis in two different places and hence y=0 will have two distinct real roots.

That is, we must have c−b2<0 in order to have two distinct real roots of x2−2bx+c=0.

This condition is necessary and sufficient

Answer 2

Answer:

hope so it will helpful to you