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The integral values of x for which x^2 +...

The integral values of x for which `x^2 +17x+71` is perfect square of a rational number are a and b, then `|a-b|`=

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VIKAS GUPTA (BLACK BOOK)-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If the equatio (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then ...

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  2. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

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  3. The integral values of x for which x^2 +17x+71 is perfect square of a ...

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  4. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

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  5. The number of real values of 'a' for which the largest value of the fu...

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  6. The number of all values of n, (whre n is a whole number ) for which t...

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  7. The number of negative intergral values of m for which the expression ...

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  8. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  9. The smallest value of k, for which both the roots of the equation, x^2...

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  10. If (x^2- 3x + 2) is a factor of x^4-px^2+q=0, then the values of p...

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  11. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

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  12. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  13. Find the number of integral vaues of 'a' for which the range of functi...

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  14. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  15. Let p (x) be a polynomial equation of least possible degree, with rati...

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  16. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

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  17. Let p (x) be a polynomial with real coefficient and p (x)=p'(x) =x^(2)...

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  18. Find the smallest positive integral value of a for which the greater r...

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  19. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

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  20. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

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