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The smallest possible natural number n, ...

The smallest possible natural number n, for which the equation `x^(2) - nx + 2014 = 0` has integral roots, is

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RESONANCE-EQUATIONS -EXERCISE-2 (PART-I: PREVIOUS ASKED QUESTION FOR PRE RMO)
  1. Three real numbers x, y, z are such that x^(2) + 6y =-17, y^(2) + 4z=1...

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  2. Let f(x) = x^3 - 3x + b and g(x) = x^2 + bx - 3 where b is a real numb...

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  3. The smallest possible natural number n, for which the equation x^(2) -...

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  4. Natural numbers k,l,p and q are such that if a and b are roots of x^(2...

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  5. Let x(1),x(2) , x(3),..........x(2014) be real numbers different from ...

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  6. If real numbers a, b, c, d, e satisfy a+1=b + 2 = c+ 3 = d + 4 = e + 5...

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  7. The equations x^2 - 4x + k = 0 and x^2 + kx -4 = 0 where k is a real n...

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  8. Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b -...

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  9. Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^...

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  10. Suppose x^(2)-x +1 is factor of 2x^(6) - x^(5) + ax^(4) + x^(3)+bx^(2)...

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  11. Let P(x) = (x - 3)(x - 4)(x - 5). For how many polynomials Q(x). does ...

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  12. Find the sum of all those integers n for which n^2+20n+15 is the squar...

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  13. Let a and p be the roots of equation x^2 + x - 3 = 0. Find the value o...

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  14. Let x^3 + ax + 10 = 0 and x^3 + bx^2 + 50 = 0 have two roots in common...

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  15. For real numbers x and y, let M be the maximum value of expression x^4...

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  16. Between 5pm and 6pm, I looked at my watch mistaking the hour hand for ...

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  17. Suppose a, b are positive real numbers such that asqrt(a) + b sqrt(b) ...

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  18. Let a, b be integers such that all the roots of the equation (x^2 + ax...

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  19. In a class, the total numbers of boys and girls are in the ratio 4 : 3...

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  20. If the real numbers x, y, z are such that x^2 + 4y^2 + 16z^2 = 48 and ...

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