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If f(x) =Pi(i=1)^3(x-ai) + sum(i=1)3 ai ...

If `f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x` where `a_i < a_(i+1)` for i = 1,2, then f(x) = 0 have

A

only one distinct real root

B

exactly two distnict real roots

C

exactly 3 distinet real roots

D

3 equal real roots

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The correct Answer is:
C
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VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f(x) =Pi(i=1)^3(x-ai) + sum(i=1)3 ai - 3x where ai < a(i+1) for i =...

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  2. Let f(x) = ax^2 + bx + c where a,b,c are integers. If sin\ pi/7 * sin\...

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

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

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

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

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

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  8. The integral values of x for which x^2 +17x+71 is perfect square of a ...

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

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

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

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

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  13. If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 w...

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  14. The smallest value of k for which both the roots of the equation x^2-8...

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

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

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  17. The curvey y = (a +1) x ^(2) + 2 meets the curve y = ax +3, a ne -1 in...

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

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

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  20. Let p (x) be a polynomial equation of least possible degree, with rati...

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

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