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If m, n be natural numbers and (x^(2)-n)...

If m, n be natural numbers and `(x^(2)-n)` be a factor of the polynomial `(ax^(2m)+bx^(2m+1)-1)`, then prove that `a=(1/n)^(m)andb=0`.

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.4
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  13. Show that the polynomial (x^(71)+1) is not divisible by (x - 1), but i...

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  15. Prove that the polynomial (x^(-19)+y^(-19)) is not divisible by (x - y...

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  16. If (x + p) be a common factor of both the polynomials (x^(2)+ax+b)and(...

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  17. What is the condition that the polynomial {x^(2)+(p+q)x+r} is divisibl...

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  18. Determine the condition for which the polynomial x^(3)+(p-q)x+r is div...

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  19. Determine the relation between c and d if (x - 2) and (x-1/2) be the t...

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  20. If the ratio of the remainders when the polynomial (x^(2m)+1) is succe...

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