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Let f(x) = ax^2 + bx + c where a,b,c are...

Let `f(x) = ax^2 + bx + c` where `a,b,c` are integers. If `sin\ pi/7 * sin\ (3pi)/7 + sin\ (3pi)/7 * sin\ (5pi)/7 + sin\ (5pi)/7 * sin\ (pi)/7=f(cos\ (pi)/7)`. then find the value of `f(2):`

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

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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, wher...

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

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  5. If the equatio (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 +17x+71 is perfect square of a ...

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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 the roots of the equation, x^2...

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

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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) be a polynomial equation of least possible degree, with rati...

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  20. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

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