Answer: Positive roots = 1
Negative real root =0 or 2
complex roots=0 or 2
Step-by-step explanation:
Given cubic polynomial f(x) = [tex]4x^3 + x^2 + 10x - 14[/tex]
By Descartes rules of signs
as this polynomial is already arranged in descending order and has only 1 sign change which means it has 1 positive real root.
Now change signs of coefficients of odd powered terms we get
[tex]-4x^3 + x^2 - 10x - 14[/tex] then we have 2 sign changes which gives 2 or zero negative real roots .
For complex roots , we know that it is a cubic polynomial i.e. it has exactly 3 roots and complex roots always occur in pair, Therefore it will have zero or 2 complex roots.
