Question

If the zeros of the polynomial x2+4x+2a are a and 2|a the zeroes of polynomial x2+ 4x+2a,a and 2|a then find the value of a​

Answer 1

Answer:

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

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

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

( 2α + α ) / 2 = 4

3α = 8

α = 8 / 3

α² = 64 / 9 -----( 1 )

Product of the zeroes = c / a

α × α / 2 = 2a / 1

α² = 4a -------( 2 )

Therefore ,Equation ( 1 ) = equation ( 2 )

64 / 9 = 4a

64 / ( 9 × 4 ) = a

16 / 9 = a

a = 16 / 9