Question

if one zero of 3x square +8x +k be the reciprocal of the other, then k=​

Answer 1

Answer:

k = 3

Step-by-step explanation:

Given, one zero of ( 3x^2 + 8x + k ) be the reciprocal of the other

Let the zeroes of given polynomial are a & 1/a

If α , β are the zeroes of a quadratic polynomial

ax^2 + bx + c , then it can be written as

ax^2 + bx + c = k ( x - α ) ( x - β )

Let the zeroes of given polynomial are a & 1/a

=> 3x^2 + 8x + k = 3 ( x - a ) ( x - 1/a )

=> 3x^2 + 8x + k = 3 ( x^2 - ax - x/a + 1 )

=> 3x^2 + 8x + k = 3 [ x^2 - ( a + 1/a )x + 1 ]

=> 3x^2 + 8x + k = 3x^2 - 3( a + 1/a )x + 3

Comparing like terms,

- 3( a + 1/a ) = 8 and k = 3