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On dividing 3x^(3)+x^(2)+2x+6 by a polyn...

On dividing `3x^(3)+x^(2)+2x+6` by a polynomial g(x), the quotient and remainder are (3x-5) and (3x+21) respectively. Find g(x).

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The correct Answer is:
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g(x)`=x^(2)+2x+3`
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NAGEEN PRAKASHAN-POLYNOMIALS-Exercise 2b
  1. Verify that 1,-2,4 are zeroes of the cubic polynomial x^(3)-3x^(2)-6x+...

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  2. Verify that 1,-2, and 1/2 are zeroes of 2x^3+x^2-5x+2. Also verify the...

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  3. Find a cubic polynomial whose zeroes are 5,6 and -4.

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  4. Find a cubic polynomial whose zeroes are (1)/(2),1 and -1.

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  5. Find the cubic polynomial with the sum, sum of the products of its zer...

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  6. Find the quotient and remainder in each of the following and verify th...

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  7. By actual division show that x+2 is a factor of x^(3)+4x^(2)+3x^(2)-20...

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  8. On dividing 3x^(3)+x^(2)+2x+6 by a polynomial g(x), the quotient and r...

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  9. If 1 is a zero of the polynomial x^(3)-4x^(2)-7x+10, find its other tw...

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  10. If two zeroes of the polynomial x^4+3x^3-20x^2-6x+36 are sqrt2 and -sq...

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  11. Find all the zeros of the polynomial x^4+x^3-34^2-4x+120,

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  12. 13. find all zeroes of 2x^4-3x^3-3x^2+6x-2 , if you know that two of i...

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  13. Find all zeroes of the polynomial 2x^4-9x^3+5x^2+3x-1 if two of its ze...

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  14. Obtain all zeros of (3x^4 -15x^3 + 13x^2 +25x -30), if two of its zero...

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  15. 012 if -5 and 7 are zeroes of x^4- 6x^3- 26x^2 +138x-35 find the other...

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  16. If the zeroes of the polynomial x^3-3x^2+x+1 are a"\ ""\ "b ,"\ "a ,"\...

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  17. Find zeroes of the polynomial f(x)=x^(3)-13x^(2)+32x-60, if it is give...

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  18. What must be added to p(x0=4x^(4)-5x^(3)-39x^(2)-46x-2, so that the re...

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  19. What must be added to 11t^(3)+5t^(4)+6t^(5)-3t^(2)+t+5, so that the re...

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  20. If alpha, beta, gamma are zeroes of polynomial 6x^(3)+3x^(2)-5x+1, the...

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