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The real values of a for which the quadr...

The real values of a for which the quadratic equation `2x^2-(a^(3)+8a-1)x+a^(2)-4a=0` possesses roots of opposite signs are given by :

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`0 lt a lt 4`
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RESONANCE-EQUATIONS -EXERCISE-1 (PART -1: PRE RMO)
  1. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. a and b are the roots of the quadratic equation x^2 + lambdax - 1/(2la...

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  17. The remainder obtained when the polynomial x+x^(3)+x^(9)+x^(27)+x^(81)...

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  18. If x, y are positive real numbers satisfying the system of equations x...

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  19. If a, b, c are positive integers such that a^2+ 2b^2-2ab = 169 and 2bc...

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  20. P = 2008^(2007) - 2008, Q = 2008^(2) + 2009. The remainder when P is d...

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