Question

polynomial x^2-5x+6 find the value of alpha^2-beta^2???

Answer 1

Answer:

Step-by-step explanation:

x^2-5x+6

alpha +beta= -b/a=  5                (alpha -beta)^2 = (alpha +beta)^2 - 4(alpha.beta)

alpha.beta = c/a = 6/1 =6                                     = 25 - 24 = 1

alpha^2-beta^2 =  (alpha +beta)(alpha -beta)

                           =  5 (1)

                           =5

Answer 2

Answer:

Step-by-step explanation:

Hey there!

Since alpha^2- beta^2 can be associated with the identity a^2-b^2 , it can be rewritten as (a+b)(a-b)

So we know that for a quadratic equation ,we can split the middle term to be the roots.

So..

x^2-5x+6

x^2 -3x-2x +6

x(x-3)-2(x-3)

(x-3)(x-2)

therefore x=3,2

The two roots of this quadratic equation are 3 and 2

Alpha=3 and beta =2

So..

Alpha^2- beta^2 will become..

3^2-2^2

9-4

5.

There you've got the answer.:-)