Question

if one zero of (a^4+4)x^2+13x+4a is reciprocal of other. find a

Answer 1

Hi ,

( plz check the problem again , constant

term may be 4a^2 )

let p( x ) = ( a^4 + 4 )x^2 + 13x + 4a^2

according to the problem

one zero is reciprocal to another.

let

one zero = p

second zero = 1/ p

product of the zeroes

= constant / ( x^2 coefficient )

p × 1/ p = ( 4a^2 )/ ( a^4 + 4 )

1 = ( 4a^2 )/ ( a^4 + 4 )

a^4 + 4 = 4a^2

a^4 - 4a^2 + 4 = 0

( a^2 )^2 - 2 × a^2 × 2 + 2^2 = 0

(a^2 - 2 )^2 = 0

Therefore,

a^2 - 2 = 0

a^2 = 2

a = + or - (sqrt 2)

i hope this will useful to you.

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