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35. Find the condition that r + (p + qx + a is divisibleby (x + p + 9)

Answer»

Let f(x) = x^3 + (p+q) x + a. We use Remainder theorem to derive our result.

Now for (x + p + q) to be a factor of f(x), f(-[p+q]) should be equal to zero.

=> -(p+q)^3 + (p+q)[-(p+q)] + a = 0.

=> a = (p+q)^2 + (p+q)^3

=> a = (p+q+1)(p+q)^2


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