Question

4. α, β are the roots of the quadratic polynomial p(x) = x2 – (k + 6)x + 2(2k-1). Find the value of k, if α + β =1/2 αβ.

Answer 1

Heya !!!


P(X) = X²-(K+6)X+2(2K-1)


Here,


A = 1 , B = -(K+6) and C = 2(2K-1)



Sum of zeroes = -B/A


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


Alpha + Beta = K +6


And,


Product of zeroes = C/A


Alpha × Beta = 4K - 2/1


Alpha × Beta = 4K-2



According to question,



Sum of zeroes = 1/2 ×Product of zeroes



Alpha + Beta = 1/2 × ( Alpha × Beta)


K + 6 = 1/2 × (4K-2)


K +6 = 4K-2/2


2(K+6) = 4K-2


2K +12 = 4K -2


4K -2K = 12+2


2K = 14


K = 14/2 => 7



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