Question

the zeros of the quadratic polynomial x square -(K + 6 )X + 2(2 k - 1) find the value of k if alpha and beta = half alpha×beta​

Answer 1

Let α and β are the roots of given quadratic equation x² - ( k +6)x + 2(2k +1) = 0 [ you did mistake in typing of equation , I just correct it ]

Now, sum of roots = α + β = - {-( k + 6)}/1 = (k + 6)
product of roots = αβ = 2(2k + 1)/1= 2(2k + 1)

A/C to question,
sum of roots ( zeros ) = 1/2 × products of roots zeros
⇒ (k + 6) = 1/2 × 2(2k + 1)
⇒ (k + 6) = (2k + 1)
⇒ k + 6 = 2k + 1
⇒ k = 5

Hence, k = 5