Question

If the zeroes of the polynomial x2 + 4x + 2k are α and 2/α then find the value of k.

Answer 1

Answer:

k = 16 / 9

Step-by-step explanation:

Compare x² + 4x + 2k with ax² +bx + c ,

a = 1 , b = 4 , c = 2k

According to the problem given ,

α and α / 2 are the zeroes of the polynomial ,

1 ) sum of the zeroes = - b / a

α + α/ 2 = - 4 / 1

( 2k + α ) / 2 = 4

3α = 8

α = 8 / 3

α² = 64 / 9 -----( 1 )

Product of the zeroes = c / a

α × α / 2 = 2k / 1

α² = 4k -------( 2 )

Therefore ,

Equation ( 1 ) = equation ( 2 )

64 / 9 = 4k

64 / ( 9 × 4 ) = k

16 / 9 = k

k = 16 / 9