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If x in R then (x^(2)+2x+a)/(x^(2)+4x+3a...

If x `in` R then `(x^(2)+2x+a)/(x^(2)+4x+3a)` can take all real values if

A

`a in (0,2)`

B

`a in [0,1]`

C

`a in [-1,1]`

D

none

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The correct Answer is:
B
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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 4
  1. If x^(2)+2ax+10 -3a gt 0 for all x in R, then

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  2. The expression y=ax^(2)+bx+c has always the same sign as of a if

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  3. If the graph of the function y=16x^(2)+8(a+5) x-7a-5 is strictly above...

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  4. Let f(x) be a quadratic expression possible for all real x. If g(x)=...

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  5. If x^(2)-2 (4 lamda-1) x+ (15 lamda^(2)-2 lamda -7) gt 0 for all real ...

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  6. If the equation x^(3 )-3x+a=0 has distinct roots between 0 and 1, then...

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  7. If c gt0 and 4a+clt2b then ax^(2)-bc+c=0 has a root in the interval

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  8. If y= tan x cot 3x, x in R, then

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  9. If a lt b lt c lt d, then the quadratic equation (x-a) (x-c) +2(x-b) (...

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  10. Let a,b,c in R and a ne 0. If alpha is a root a^(2) x^(2) +bx+c=0, bet...

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  11. If the roots of the equation x^(2)+2ax+b=0 are real and distinct and t...

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  12. The middle point of the interval in which x^(2)+2 (sqrt(x))^(2)-3 le 0...

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  13. If x in R , the least value of the expression (x^(2)-6x+5)/(x^(2)+2...

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  14. The inequality (x^(2)-|x|-2)/(2|x|-x^(2)-2) gt 2 holds only if.

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  15. If x is real, then (x^(2)-2x+4)/(x^(2)+2x+4) takes values in the inter...

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  16. If x is real, the maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is :

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  17. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

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  18. If x in R then (x^(2)+2x+a)/(x^(2)+4x+3a) can take all real values if

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  19. The values of p for which the expression (px^(2)+3x-4)/(p+3x-4x^(2)) c...

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  20. If P (x) is a polynomial of degree less than or equal to 2 and S is th...

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