if one zero of p(x)=(a square+4)x square+13x+4a is the reciprocal of the other then find the value of a

Asked by sanjaypadmanabhan99 | 3rd Apr, 2014, 12:24: PM

Expert Answer:

let the zeros be alpha and beta then for equation

ax2 + bx + c = 0

   beta  = 1/alpha (given)

   alpha + beta = -b/a = alpha + 1/alpha

                                       = alpha2 + 1  / alpha

 alpha x beta = c/a = alpha x 1/alpha

                                 = 1

by comparision c = a

a2 + 4 = 4a

a2 + 4 - 4a = 0

(a+2)     = 0

then a = -2 

Answered by  | 3rd Apr, 2014, 12:50: PM

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