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A quadratic equations p(x)=0 having coef...

A quadratic equations `p(x)=0` having coefficient `x^(2)` unity is such that `p(x)=0` and `p(p(p(x)))=0` have a common root, then

A

A. `p(0) p(1) gt 0`

B

B. `p(0) p(1) lt 0`

C

C. `p(0) p(1) = 0`

D

D. `p(0)=0` and `p(1)=0`

Text Solution

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The correct Answer is:
C
`(c )` let `p(x)=x^(2)+ax+b` and let `alpha` be the common root
`:. P(alpha)=0` and `p(p(p(alpha)))=0impliesp(p(0))=0`
`implies p(alpha)=0`
Now `p(0)=b`
`:. P(b)=0` ,brgt `implies b^(2)+ab+b=0`
`implies b(b+a+1)=0`
`implies p(0)p(1)=0`
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