Question

If $\alpha$ is a complex constant such that $\alpha$$z^2$ + z + $\overline{\alpha }$ = 0 has a real root.Find the value of real root.

• A. 1
• B. -1
• C. 0
• D. All of these

Answer 1

Answer: (A), (B)

The correct options are
A

1

B

-1

$\alpha$$z^2$ + z + $\overline{\alpha }$ = 0

Let $\alpha$ = x + iy

(x + iy)$z^2$ + z + (x - iy) = 0

Let the real root is p

(x + iy)$p^2$ + p + (x - iy) = 0

(x$p^2$ + p + x) + (y$p^2$ - y)i = 0

Comparing real and imaginary part on both sides

y$p^2$ - y = 0

$p^2$ = 1

p = $\underset{–}{+}1$

Real root = $\underset{–}{+}1$.