How to calculate nothing?

Algebra Level 3

We know that by Vieta's formula , the sum of roots of the equation $x^5 + 4x^4 + 3x^3 + 2x^2 + x + 1 = 0$ is -4. But what about the sum of positive roots of the same equation?

The answer is 0.

2 solutions

Kushal Bose
Dec 4, 2016

The function $f(x)=x^5+4 x^4+3 x^3+2 x^2+x+1$ .The value of $f(0)=1$ .

For every $x \geq 0$ the function will surely give positive value because every co-efficient is postive.So it will never intersect or cross $X-$ axis.So the number of positve roots are zero.Thus the sum of positive roots is zero.