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?

Expert Answers
hala718 eNotes educator| Certified Educator

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:

ax^3+bx^2+cx+d=0

Viete' relation states that:

x1+x2+x3= -b/a

Then in our equation:

a= 1

b=-3

c=2

d=0

Then x1+x2+x3= -b/a= 3

giorgiana1976 | Student

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

neela | Student

 

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