Question

if alpha and beta are the zeros of polynomial P of x is equal to 2 X square + 5 x + ki satsi find the relation Bita squire Plus Alpha square plus alpha beta equal to 21 by 7 then find the value of k​

Answer 1

Step-by-step explanation:

Given if alpha and beta are the zeros of polynomial P of x is equal to        2 x^2 + 5 x + k satisfying the relation Beta^2+ Alpha^2 plus alpha beta equal to 21 / 7 then find the value of k

• Now p(x) = 2x^2 + 5x + k
• So p(α) = f (β) = 0
• Now sum of roots α + β = - 5/2  (- coefficient of x / coefficient of x^2)
• Also product αβ = k/2 (coefficient of constant term / coefficient of x^2)
• So now we need to satisfy the relation  
•                    α ^2 + β^2 + αβ = 21/7  
•                   (So (α + β)^2 = α^2 + β^2 + 2αβ)
•       Now we can write the equation as
•                      (α + β)^2 - 2αβ + αβ = 21 / 7
•                       (-5/2)^2 – k/2 = 3
•                        25/4 – k/2 = 3
•                       25 – 2k = 12
•                      25 – 12 = 2k
•                       2k = 13
•                    Or k = 13/2

Reference link will be

https://brainly.in/question/8667628

Answer 2

• alpha ² +beta² = (alpha +beta )² = 2ALPHA beta
• x²-5x+6( -5/2 )² - k/2 = 3

1. 25/4 - k /2 =3
2. 25-2k=12

• 25-2k=12
• 25-12=2k

1. 2k=13
2. k=13
3. the correct option is c.) 13 or 13/2