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If both (x-2) and ( x- (1)/(2)) are the ...

If both (x-2) and `( x- (1)/(2))` are the factors of `ax^(2) + 5x + b `, then show that a =b .

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The correct Answer is:
`:.a = b` Hence it is proved.
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SURA PUBLICATION-ALGEBRA-EXERCISE 3.3
  1. Find the remainder when 3x^(3) - 4x^(2) + 7x -5 is dividend by ( x + ...

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  2. What is the remainder when x^(2018) + 2018 is divided by x-1 .

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  3. For what value of k is the polynomial p(x) = 2x^(3) -kx^(2) + 3x + 10 ...

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  4. If two polynomials 2x^(3) + ax^(2) + 4x -12 and x^(3) +x^(2) - 2x + a...

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  5. Determine whether (x-1) is a factor of the following polynomials : ...

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  6. Determine whether (x-1) is a factor of the following polynomials : x...

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  7. Using factor theorem, show that (x-5) is a factor of the polynomial 2x...

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  8. Determine the value of m, if (x+ 3) is a factor of x^(3) -3x^(2) - mx ...

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  9. If both (x-2) and ( x- (1)/(2)) are the factors of ax^(2) + 5x + b , t...

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  10. If ( x-1) divides the polynomial kx^(3) - 2x^(2) + 25 x -26 without re...

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  11. Check if ( x+ 2) and ( x-4) are the sides of a rectangle whose area is...

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  12. Find the remainder using remainder theorem , when 4x^(3) - 5x^(2) +...

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  13. Find the remainder using remainder theorem , when x^(3) - 7x^(2) - ...

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  14. Find the value of a if 2x^(3) - 6x^(2) + 5ax - 9 leaves the remainder ...

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  15. If the polynomials f(x) = ax^(3) + 4x^(2) +3x - 4 and g(x) = x^(3) -4...

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  16. Show that x + 4 is a factor of x^(3) + 6x^(2) - 7x - 60

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  17. In ( 5x + 4) a factor of 5x^(3) + 14x^(2) - 32 x - 32

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  18. Find the value of k, if (x -3 ) is a factor of polynomials x^(3) - 9x^...

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  19. Show that ( x- 3) is a factor of x^(3) + 9x^(2) -x - 105

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  20. Show that (x+ 2) is a factor of x^(3) -4x^(2) - 2x + 20

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