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Let p and q be non-zero integers. Co...

Let p and q be non-zero integers.
Consider the polynomial
`A(x)=x^(2)+px+q`
It is given that `(x-m) and (x-km)` are simple factors of A(x), where m is a non-zero integer and k is a positive integer, `k ge 2`. Which one of the following is correct?

A

`(k+1)^(2) p^(2) =kq`

B

`(k+1)^(2)q=kp^(2)`

C

`k^(2)q=(k+1)p^(2)`

D

`k^(2)p^(2)=(k+1)^(2)q`

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Knowledge Check

  • If 6 ge x ge -2 and 4 ge y ge -4 , find the limits for (y)/(x) , where x and y are non-zero integers.

    A
    `(y)/(x) ge 2, (y)/(x) le (2)/(3)`
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    `(y)/(x) ge (-2)/(3), (y)/(x) le 2`
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    `(y)/(x) ge (-2)/(3), (y)/(x) le (1)/(4)`
    D
    `(y)/(x) ge -4, (y)/(x) le 4`

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