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If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a), t...

If `f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a)`, then prove that f(a) + f(b) = a + b.

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.4
  1. If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a), then prove that f(a) + f(b) = a...

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  2. If p(x) be a polynomial such that p(-a/b)=0, then one of the factor of...

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  3. If the polynomial f(x)=2x^(3)+kx^(2)+11x+k+3 be divisible by (2x - 1),...

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  4. If (x - a) be a factor of f(x), but is not a factor of g(x), where bot...

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  5. If (x^(2)-1) be a factor of the polynomial f(x)=ax^(4)+bx^(3)+cx^(2)+d...

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  6. (x + a) will be a factor of the polynomial p(x)=x^(n)+a^(n), when-

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  7. If x be a factor of the polynomial f(x) = (x - a) (x + b) (x - c), the...

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  8. If (x+sqrt11) be a factor of f(x)=x^(3)+k, then k =

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  9. If (x^(2)+r) be a factor of the polynomial f(x)=x^(3)-rx^(2)+rx-r^(2),...

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  10. If f(x)=2x^(3)+9x^(2)+x+k and g(x) = x -1 be two polynomials, then g(x...

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  11. Which one of the followings is a factor of the polynomial p(x)=x^(4)-1...

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  12. Find the value of a if (1 - 2x) is a factor of the polynomial (2x^(4)-...

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  13. Find the value of k if (x - 2) is a factor of the polynomial (2x^(5)-6...

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  14. If (x + 1) be a factor of the polynomial (x^(43)+kx+2), determine the ...

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  15. If (x + 1) be a factor of the polynomial (x^(200)+2x^(201)+k), then de...

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  16. If n be an odd negative integer, then prove that (x + 1) is a polynomi...

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  17. Prove that the polynomial (x^(5)-y^(5)) is not divisible be (x + y).

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  18. Is the polynomial (x^(101)+1) divisible by (x + 1) ? Give reasons in f...

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  19. Examine whether (x + y) is a factor of the polynomial (x^(11)+y^(11)) ...

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  20. If (x + 2y) be a factor of the polynomial (x^(2)+4xy+4y^(2)), find the...

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  21. If (x-sqrt11) be a factor of the polynomial of f(x), but not a factor ...

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