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If 'a' and 'b' are unequal and x^2+ ax+b...

If `'a'` and `'b'` are unequal and `x^2+ ax+b` and `x^2+bx+a` have a common factor, then the value of `(a+b)` is
(1)`-1` (2) `0` (3)`1` (4) `2`

Text Solution

Verified by Experts

Here, `f(x) = x^2+ax+b`
`g(x) = x^2+bx+a`
Let `(x-p)` is a common factor for both polynomials.
Then, `f(p) = p^2+ap+b =0`
`g(p) = p^2+bp+a = 0`
Subtracting above polynomials,
`p^2+ap+b-p^2-bp-a = 0`
...
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