Question

If , and are the zeroes of the cubic polynomial

3 − 4

2 + 5 − 2 , then

alpha+beta+gama=??​

Answer 1

Correct Question :

If α , β and γ are the zeroes of the cubic polynomial, x³ - 4x² + 5x - 2 ;

then α + β + γ = ?

Answer :

α + β + γ = 4

Step-by-step explanation :

⇒ Cubic Polynomial : -

• It is a polynomial of degree 3.

• General form :

       ax³ + bx² + cx + d

• Relationship between zeroes and coefficients :

          ☆ Sum of zeroes

                       = -(x² coefficient)/x³ coefficient

                       = -b/a

          ☆ Sum of the product of zeroes taken two at a time

                       = x coefficient/x³ coefficient

                       = c/a                          

          ☆ Product of zeroes

                      = -(constant term)/x³ coefficient

                      = -d/a

______________________________

Given polynomial,

x³ - 4x² + 5x - 2

It is of the form ax³ + bx² + cx + d

a = 1 , b = -4 , c = 5 , d = -2

∵ α + β + γ = sum of zeroes

⇒ Sum of zeroes = -b/a

                             = -(-4)/1

                             = 4

      ∴ α + β + γ = 4

____________________________

Also,

• αβ + βγ + γα = c/a

                             = 5/1

                             = 5

• αβγ = -d/a

               = -(-2)/1

               = 2