Question

.
(ii
) If a and ß are the zeroes of the quadratic polynomial
p(x)=x*-(k+6)x + 2(2k-1). Find the value of k, if a+b ==1/2 aß.​

Answer 1

Answer:

k = 7

Step-by-step explanation:

p(x) = x^2 - (k+6)x + 2(2k-1)

[a=1, b= -(k+6), c= 2(2k-1)]

α+β= 1/2αβ (given)

By relations with roots and coefficients,

i) α+β = -b/a

  α+β = k+6    ------------- 1

ii) αβ = c/a

   αβ = 2(2k-1)

   1/2(αβ) = 2k-1                 (divide by 2 on both side)

   α +β = 2k-1                     (∵ α+β = 1/2 αβ)

   k + 6 = 2k -1                   ( from 1)

∴  k= 7