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If 3x^(2)+4kx+1 gt 1 for all real value...

If `3x^(2)+4kx+1 gt 1` for all real values of x, then k lies in the interval

A

`((-sqrt(3))/(2), (sqrt(3))/(2))`

B

`((-1)/(4), (1)/(4))`

C

`[(-sqrt(3))/(2), (sqrt(3))/(2)]`

D

`((-1)/(2), (1)/(2))`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-QUADRATIC EQUATIONS & EXPRESSIONS-EXERCISE-II
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  4. I) For x in (2, 4) the sign of x^(2)-6x+5 is negative II) For x in ...

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  6. If x^(2)+bx+x=0 has no real roots and a+b+c lt 0 then

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  7. Assertion (A): The maximum value of log(1//3)(x^(2)-4x+5) is zero Re...

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  8. Assertion (A), The equation x^(2)+ 2|x|+3=0 has no real root. Reas...

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  9. Assertion(A): x^(2)+x+1 gt 0 for all positive real values of x only. ...

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  10. If x^(2)+4xy+4y^(2)+4x+cy+3 can be written as the product of two linea...

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  11. If x^2 + 4y ^2 - 8x +12 =0 is satified by real values of x na...

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  12. In a triangle PQR angle R=(pi)/(4), if tan (p/3) and tan ((Q)/...

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  13. The product of real roots of the equation |x|^(6//5)-26|x|^(3//5...

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  14. alpha , beta are the roots of ax ^2+bx +c=0 and gamma , sigma...

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  15. If alpha, beta are the roots of x^(2)- p(x+1)-c=0 then (alpha^(2)+2alp...

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  16. IF a = cos ( (2 pi ) /(7)) + isin ((2pi)/(7)) , alpha = a + a^2+a^...

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  17. The roots of (x-b)(x-c) +(x-a)(x-c) +(x-a) (x-b)=0 are

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  18. Given that for all real x, the expression (x^(2)-2x+4)/(x^(2)+2x+4) li...

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  19. If a,b,c are the sides of a triangle then the range of (a^(2)+b^(2)+c^...

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  20. If the equation (cos p - 1)x^(2) + cos p x + sin p =0 in the varable x...

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