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Consider the equation x ^(3) -ax ^(2) +...

Consider the equation ` x ^(3) -ax ^(2) +bx-c=0,` where a,b,c are rational number, `a ne 1.` it is given that ` x _(1), x _(2) and x _(1)x_(2)` are the real roots of the equation. Then `x _(1) x _(2) ((a +1)/(b +c))=`

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VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Find the number of positive integral values of k for which kx ^(2) +(k...

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