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

Question

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 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. `p(0) p(1) gt 0`
B. `p(0) p(1) lt 0`
C. `p(0) p(1) = 0`
D. `p(0)=0` and `p(1)=0`

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

6 views Answered 2023-02-05 15:29