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Question

If α is a complex constant such that αz2 + z + ¯¯¯¯α = 0 has a real root.Find the value of real root.


  1. 1

  2. -1

  3. 0

  4. All of these


Solution

The correct options are
A

1


B

-1


 αz2 + z + ¯¯¯¯α = 0

Let α = x + iy

(x + iy)z2 + z + (x - iy) = 0

Let the real root is p

(x + iy)p2 + p + (x - iy) = 0

(xp2 + p + x) + (yp2 - y)i = 0

Comparing real and imaginary part on both sides 

                 yp2 - y = 0

                  p2 = 1

              p = +1

Real root = +1.

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