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Consider the equation (x^2 + x + 1)^2-(m...

Consider the equation `(x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1),` where `m` is a real parameter. By putting `x^2+x+1=t--(2)` then `t >= 3/4` for real `x` the equation can be transferred to `f(t) = t^2- (m-3)t + m=0` . At what values of m for which the equation (1) will have real roots?

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VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let f (x) =ax ^(2) + bx+ c where a,b,c are integers. If sin ""pi/7. si...

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  2. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

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  3. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

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  4. The number of positive integral values of , m le 16 for which the equa...

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  5. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

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  6. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

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  7. The integral values of x for which x ^(2) + 17 x +7 is perfect square ...

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  8. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

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  9. The number of real values of 'a' for which the largest value of the fu...

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  10. The number of all values of n, (whre n is a whole number ) for which t...

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  11. The number of negative intergral values of m for which the expression ...

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  12. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  13. The smallest value of k for which both roots of the equation x^(2)-8kx...

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  14. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  15. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

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  16. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  17. Find the number of integral vaues of 'a' for which the range of functi...

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  18. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  19. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  20. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

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