Question

if alpha are the zeroes of the polynomial p(x)=x^2-3kx+k^2, find k^2 if alpha ^2+beta^2 =28​

Answer 1

Answer:

k² =  4

Step-by-step explanation :

x² - 3kx + k²

α + β = -b/a

= -( -3k)/1

= 3k

αβ = c/a

= k²/1

= k²

NOW,

α² + β² = ( α + β)² - 2αβ     ( using identity, (a² + b²) = (a+b)² - 2ab )

(3k²) - 2 (k²) = 28

9k² - 2k² = 28   ( α² + β² = 28)

7k² = 28

k² = 4

I HOPE THIS WILL HELP YOU OUT :)