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Algebra

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..

Meghendra Agrawal

7 Years agoGrade

2 Answers

Aditya Gupta

7 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

7 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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