Good sum

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Let a,b,p,q Îµ Q and suppose that f(x) = x² +ax+b=0
and g(x)= x³ + px + q = 0 have a common irrational root , then
(a) f(x) divides g(x)
(b) g(x) â‰¡ x f(x)
(c) g(x) â‰¡ (x-b-q)f(x)
(d) none

#Mathematics #Algebra

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Swarna Kamal Dhyawala ·2012-10-16 22:48:13

Is (a)the answer?

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Anirban Mukherjee ·2012-10-17 19:56:12

Yes...How did you conclude?

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Swarna Kamal Dhyawala ·2012-10-17 22:02:11

Let the common irrational root be (a+√b ).
and we know that irrational roots r in conjugate pairs .Therefore the other root must be (a-√b).
The quadratic equation has these two root n the cubic equation too has these two roots .Therefore
the quadratic equation divides the cubic equation.

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Good sum

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