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The quadratic equation p(x) = 0 with real coefficient has purely imaginary roots.Then the equation p(p(x)) = 0 has ​1)only purely imaginary roots 2)all real roots 3)two real and two purely imaginary roots 4)neither real nor purely imaginary roots Please explain the question and its solution..

The quadratic equation p(x) = 0 with real coefficient has purely imaginary roots.Then the equation p(p(x)) = 0 has 
​1)only purely imaginary roots
2)all real roots
3)two real and two purely imaginary roots
4)neither real nor purely imaginary roots
Please explain the question and its solution..

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2 Answers

Aditya Gupta
2081 Points
5 years ago
let p(x)=ax^2+bx+c........(1)
then p(p(x))= ay^2+by+c, where y=p(x)........(2)
now, let us assume that (2) has a real root ‘z’. as ‘z’ is real, p(z) is also real. that means (1) will have a real solution with x=p(z). but it is given that p(x) has  purely imaginary roots. so, p(p(x))=0 will have only purely imaginary roots.
option 1) is right
Aditya Gupta
2081 Points
5 years ago
actually, the roots will not be PURELY imaginary. they will be complex numbers, neither purely real nor purely imaginary

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