996Is (a)the answer?
Let a,b,p,q ε 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) ≡ x f(x)
(c) g(x) ≡ (x-b-q)f(x)
(d) none
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3 Answers
996Let 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.