JEE Advanced | 2014Quadratic EquationHard
Question
The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has
Options
A.Only purely imaginary roots
B.All real roots
C.Two real and two purely imaginary roots
D.Neither real nor purely imaginary roots
Solution
Let p(x) = x2 + a (a > 0) (∵ roots are purely imaginary)
p(p(x)) = (x2 + a)2 + a (a ∈ R)
x4 + 2a(x2) + a2 + a = 0
⇒ x2 =
= - a +
x = +
= x1 + iy1
p(p(x)) = (x2 + a)2 + a (a ∈ R)
x4 + 2a(x2) + a2 + a = 0
⇒ x2 =
= - a +
x = +
= x1 + iy1Create a free account to view solution
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