Question

If alpha, beta are roots of polynomial x^2-6x+k, find the value of k such that square of sum of alpha, beta-product of alpha, beta=40

Answer 1

Heya !!!


P(X) = X² - 6X + K



Here,



A = 1 , B = -6 and C = K


Sum of zeroes = -B/A



Alpha + Beta = -6/1



Alpha + Beta = -6 --------(1)



And,



Product of zeroes = C/A


Alpha × Beta = K/1


Alpha × Beta = K -------(2)


According to question,








( Alpha + Beta)² - ( Alpha × Beta ) = 40



( -6)² - ( K ) = 40



36 - K = 40


K = 36-40



K = -4.




HOPE IT WILL HELP YOU.,.... :-)