Question

find a quadratic polynomial whose zeros are Alpha and beta satisfy the relation alpha +beta=3 and alpha -beta=-1​

Answer 1

Answer:

x^2 - 3x + 2.

Step-by-step explanation:

Given,

       α and β are roots and follow these relations :

    α + β = 3          

    α - β = - 1

Adding both:

      α + β = 3

     α -  β = - 1

    2α      = 2  

⇒ 2α = 2

⇒ α = 1

          Therefore,

                α + β = 3

                1 + β = 3

                     β = 2

Now,

⇒ sum of roots = α + β = 3

⇒ Product of roots = αβ = 2( 1 ) = 2

Thus,

⇒ Required equation is

⇒ x^2 - Sx + P       { where S and P are sum and product of roots respectively }

⇒ x^2 - 3x + 2

Answer 2

Answer:

X^2-3x+2

Step-by-step explanation:

Alfa+beta=3

Alfa-beta=-1

(--) (+) =(+)

------------------

2beta =4

Beta =4/2

Beta =2

From eq 1

Alfa+2=3

Alfa=3--2

Alfa=1

Alfa +beta =3

Alfa×beta =2

Then the equation is x^2-x(3)+2

X^2-3x+2