Which is the value of the sum x1+x2+x3, if x1, x2, x3 are the solutions of the equation x^3-3x^2+2x=0?
The equation x^3 -3x^2 +2x =0
is a third power polynomial . Then it has 3 roots:
x1, x2, and x3
In the standard form of third power polynomial:
Viete' relation states that:
Then in our equation:
Then x1+x2+x3= -b/a= 3
We'll use the first Viete's relation, in order to calculate the sum x1 + x2 + x3.
For a polynomial ax^3+bx^2+cx+d=0,
x1 + x2 + x3 = -b/a
We'll identify the coefficients from the given polynomial:
a = 1
b = -3
c = 2
d = 0
So, calculating the sum, we'll get:
x1 + x2 + x3 = -b/a = - (-3/1)
x1 + x2 + x3 = 3
The solutions of x^3-3x^2+2x = 0. To find the sum of the solutions x1+x2+x3.
By the relation of roots and coefficients,the sum of the roots,
x1+x2+x3 = coefficient of x^2/coefficient of x^3
= -(-3)/1 = 3