hi there, just need some clarification on one point, i'll post the whole question and show you what i've done so far.
a. The polynomial 2x^3-5x^2+46x+87 has one real factor (2x+3) and two complex factors.
By algebraic division and solving a quadratic equation find the compex factors and express the above polynomial in the form 2x^3-5x^2+46x+87 = (2x+3)(x-a)(x-b) where a and b are complex numbers.
b. Calculate the gradient of the curve y=2x^3-5x^2+46x+87 at the point where it crosses the x axis
c. Show by differentiation and solving a quadratic equation that there are no points on the above curve where the gradient is 0.
The answers i got for a were (2x+3)(x-(2+j5)(x-(2-j5)
The answer i got for b was 74.5
Its part c that i'm not sure of, how can i tell the gradient never equals 0?
Any help is apprecciated!
is . (Why?)
Notice that there is a term under a square root here. This is called the discriminant, and is denoted by .
If then there are two solutions for x.
If then there is one solution for x.
If then there does not exist any solutions for x.
In your problem, .
What does equal in this case? What does this tell you about the solutions?