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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..

2 years ago

Answers : (2)

Aditya Gupta
2069 Points
							
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
2 years ago
Aditya Gupta
2069 Points
							
actually, the roots will not be PURELY imaginary. they will be complex numbers, neither purely real nor purely imaginary
2 years ago
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