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If x^2 + 3x + 5 = 0 and ax^2 + bx + c = ...

If `x^2 + 3x + 5 = 0` and `ax^2 + bx + c = 0` have a common root and `a, b, c in N`, then the minimum value of (a + b + c) is:

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RESONANCE-EQUATIONS -EXERCISE-1 (PART -1: PRE RMO)
  1. If the two equations x^2 - cx + d = 0 and x^2- ax + b = 0 have one com...

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  2. If x^2 + 3x + 5 = 0 and ax^2 + bx + c = 0 have a common root and a, b,...

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  3. x^2 + x + 1 is a factor of ax^(3) + bx^2 + cx + d = 0, then the real r...

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  4. If roots of equation 2x^(4) - 3x^(3) + 2x^2 - 7x -1 = 0 are alpha, bet...

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  5. If two roots of x ^(3) -ax ^(2) + bx -c =0 are equal in magnitude but ...

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  6. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

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  7. If the inequality (m-2)x^(2)+8x+m+4gt0 is satisfied for all x epsilon ...

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  8. The real values of a for which the quadratic equation 2x^2-(a^(3)+8a-1...

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  9. If a, p are the roots of the quadratic equation x^2 - 2p (x - 4) - 15 ...

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  10. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

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  11. Each root of the equation ax^2 + bx + c = 0 is decreased by 1. The qua...

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  12. x,y,z are distinct real numbers such that x+1/y = y + 1/z =z + 1/x Th...

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  13. A hare sees a hound 100 m away from her and runs off in the opposite d...

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  14. a and b are positive integers that a^(2) + 2b = b^(2) + 2a +5. The val...

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  15. a ne 0, b ne 0. The number of real number pair (a, b) which satisfy t...

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  16. The value of root(3)(5+2sqrt(13)) + root(3)(5-2sqrt(13)) is= ……………..

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  17. If a, b, c, d satisfy the equation a + 7b + 3c + 5d = 0, 8a + 4b + 6c ...

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  18. The combined age of a man and his wife is six times the combined ages ...

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  19. If (x+1)^(2) =x, the value of 11x^(3) + 8x^(2) + 8x -2 is:

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  20. If one root of sqrt(a-x) + sqrt(b+x) = sqrt(a) + sqrt(b) is 2012, th...

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