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Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2)...

Let `P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, delta` are the roots of the equation `x ^(4) -x ^(3)-x ^(2) -1=0,` then `P (alpha ) + P (beta) +P (gamma) + P(delta)=`

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VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Find the smallest positive integral values of a for which the greater ...

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

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  3. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

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  4. The number of integral value of a,a, in [-5, 5] for which the equation...

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

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

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  7. If x and y are real numbers connected by the equation 9x ^(2)+2xy+y^(2...

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

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

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

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

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

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

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

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

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

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

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

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  19. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

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

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