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Let f (x) =ax ^(2) +bx+c, where a,b,c ar...

Let `f (x) =ax ^(2) +bx+c,` where a,b,c are integers and `a gt 1. If `f (x)` takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which `f (x)` takes the value 2p is :

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VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of integral value of a,a, in [-5, 5] for which the equation...

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  2. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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  3. Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x...

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  4. If and y ar real numbers connected by the equation 9x ^(2)+2xy+y^(2) -...

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  5. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

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  6. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

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  7. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

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  8. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

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  9. Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+...

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  10. The number of ordered pairs (a,b) where a,b are integers satisfying th...

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  11. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

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  12. If the range of the values of a for which the roots of the equation x ...

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  13. Find the number of positive integers satisfying the inequality x^(2) -...

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  14. If sin theta and cos theta are the roots of the quadratic equation ax...

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  15. Let the inequality sin ^(2) x+a cos x +a ^(2) ge1+ cos x is satisfied...

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  16. alpha and beta are roots of the equation 2x ^(2)-35x+2=0. Find the val...

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  17. The sum of all integral values of 'a' for which the equation 2x ^(2) -...

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  18. Let f (x) be a polynomial of degree 8 such that F ®=1/r, =1,2,3,…,8,9,...

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  19. Let alpha, beta are two ral roots of equation x ^(2) + px+ q =0, p ,q,...

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  20. If cos A, cosB and cosC are the roots of the cubic x^3 + ax^2 + bx + ...

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