Question

If one zero of the polynomial (a^2-9)x^2+13x+6a is reciprocal of the other , find a

Answer 1

Answer:

a = 3 ± 3√2.

Step-by-step explanation:

Given polynomial :

( a^2 - 9 )x^2 + 13x + 6a.

Comparing this polynomial with ax^2 + bx + c, in this polynomial, - b / a represents the sum of roots and c / a represents the product of roots.

Let the roots of given equation be d and 1 / d { since other is the reciprocal of the first one }.

From the cases given above :

= > Product of roots of given equation = 6a / ( a^2 - 9 )

= > d × 1 / d = 6a / ( a^2 - 9 )

= > 1 = 6a / ( a^2 - 9 )

= > 6a = a^2 - 9

= > a^2 - 6a - 9 = 0

= > a = [ - ( - 6 ) ± √{ ( - 6 )^2 - 4( - 9 ) } ] / 2

= > a = [ 6 ± √( 36 + 36 ) ] / 2

= > a = 3 ± 3√2

Hence the required value a is 3 ± 3√2.