Home
Class 12
MATHS
For x^2-(a+3)|x|-4=0 to have real soluti...

For `x^2-(a+3)|x|-4=0` to have real solutions, the range of `a` is
a)`(-oo,-7]uu[1,oo)`
b)`(-3,oo)`
c)`(-oo,-7]`
d)`[1,oo)`

A

`(-oo,-7]cup [1,oo)`

B

`(-3,oo)`

C

`(-oo,-7]`

D

`[1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
`a = (x^(2) + 4)/(|x|) - 3`
`= |x| + (4)/(|x|) - 3`
`ge 2 sqrt(|x| xx (4)/(|x|)) - 3`
`implies a ge 1`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|5 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Linked comprehension type|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Concept Application Eexercises 6.4|4 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real and distinct, then the value of a in a) (-oo,3] b) (-oo,-2)uu(2,oo) c) [-2,2] d) [-3,oo)

If (log)_3(x^2-6x+11)lt=1, then the exhaustive range of values of x is: (a) (-oo,2)uu(4,oo) (b) (2,4) (c) (-oo,1)uu(1,3)uu(4,oo) (d) none of these

The range of a for which the equation x^2+ax-4=0 has its smaller root in the interval (-1,2)i s a. (-oo,-3) b. (0,3) c. (0,oo) d. (-oo,-3)uu(0,oo)

Let A (0,2),B and C be points on parabola y^(2)+x +4 such that /_CBA (pi)/(2) . Then the range of ordinate of C is (a) (-oo,0)uu (4,oo) (b) (-oo,0] uu[4,oo) (c) [0,4] (d) (-oo,0)uu [4,oo)

If cosec^(-1)(cosecx) and cosec(cosec^(-1)x) are equal functions, then the maximum range of value of x is (a) [-pi/2,-1]uu[1,pi/2] (b) [-pi/2,0]uu[0,pi/2] (c) (-oo,-1)uu[1,oo] (d) [-1,0]uu[0,1]

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval a) (-oo,-4) (b) (-oo,0) c) (4,oo) (d) none of these

If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and maximum, then the range of values of t is (a) (0,4) (b) (0,oo) (c) (-oo,-11) (d) (4,oo)

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval (-oo,-4) (b) (-oo,0) (4,oo) (d) none of these

If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of values of c is (a) (2,oo) (b) (4,oo) (c) (-oo,-2) (d) (-oo,-4)

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -EXERCISES (Single Correct answer type)
  1. The minimum value of (x^(4)+y^(4)+z^(2))/(xyz) for positive real numbe...

    Text Solution

    |

  2. A rod of fixed length k slides along the coordinates axes, If it meets...

    Text Solution

    |

  3. The least value of 6tan^2varphi+54cot^2varphi+18 is 54 when A.M.geq GM...

    Text Solution

    |

  4. If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...

    Text Solution

    |

  5. If y=3^(x-1)+3^(-x-1) , then the least value of y is 2 6 2//3 3//2

    Text Solution

    |

  6. Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers...

    Text Solution

    |

  7. If the product of n positive numbers is n^n , then their sum is a posi...

    Text Solution

    |

  8. The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3...

    Text Solution

    |

  9. If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-...

    Text Solution

    |

  10. If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101...

    Text Solution

    |

  11. For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a)(-oo...

    Text Solution

    |

  12. If a ,b ,c are the sides of a triangle, then the minimum value of a/(b...

    Text Solution

    |

  13. If a,b,c,d in R^(+)-{1}, then the minimum value of log(d) a+ log(c)b+l...

    Text Solution

    |

  14. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

    Text Solution

    |

  15. If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...

    Text Solution

    |

  16. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c...

    Text Solution

    |

  17. If a ,b ,c ,d in R^+a n da ,b ,c are in H.P., then a+d > b+c a+b > c+...

    Text Solution

    |

  18. If a ,b ,c ,d in R^+ such that a+b+c=18 , then the maximum value of a...

    Text Solution

    |

  19. f(x)=((x-2)(x-1))/(x-3), forall xgt3. The minimum value of f(x) is equ...

    Text Solution

    |

  20. If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...

    Text Solution

    |