Home
Class 12
MATHS
The complete solution set of the equatio...

The complete solution set of the equation `|x^2-5x+6|+|x^2+12x+27|=|17x + 21 | ` is a.`x in [-9,3]` b.`x in [-3,2) cup (2,3] ` c.`x in [-9 , -3] cup [ 2,3]` d.`x in (-2,3)`

A

`x in [-9,3]`

B

`x in [-3,2) cup (2,3] `

C

`x in [-9 , -3] cup [ 2,3]`

D

`x in (-2,3)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `|x^2-5x+6|+|x^2+12x+27|=|17x+ 21|`
or `|x^2-5x+6|+|x^2+12x+27|`
`=|x^2+12x+27)-(x^2-5x+6)|`
`rArr (x^2-5x+6)(x^2+12x+27)le 0 `
`rArr (x-2)(x-3)(x+3)(x+9)le 0 `

From the sing scheme , `x in [-9,-3] cup [2,3]`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Archives|1 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 1.5|12 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Complete solution set of inequlaity ((x+2)(x+3))/((x-2)(x-3))le1

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x^2-5x+3)=-3/2 is

Which of the following is not the root of the equation |[x,-6,-1],[ 2,-3x,x-3],[-3, 2x,x+2]|=0? a. 2 b. 0 c. 1 d. -3

If |(12x)/(4x^(2)+9)| le 1 , then (a) x in R (b) x in [-3,3] (c) x in [-1,oo) (d) x in (-oo,2]

The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is a. -1 b. 1 c. -6 d. 6

The complete solution set of inequality ((x-5)^(1005)(x+8)^(1008)(x-1))/(x^(1006)(x-2)^3(x-3)^5(x-6)(x+9)^(1010)) le 0

The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3x))^9

If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then the set of values of x is

The maximum slope of the curve y=-x^3+3x^2+9x-27 is (a) 0 (b) 12 (c) 16 (d) 32

CENGAGE PUBLICATION-SET THEORY AND REAL NUMBER SYSTEM -EXERCISES
  1. Which is the simplified representation of (A' cap B' cap C) cup (B cap...

    Text Solution

    |

  2. In a statistical investigation of 1,003 families of Calcutta, it was f...

    Text Solution

    |

  3. A survey shows that 63 % of the pepole watch a news channel whereas , ...

    Text Solution

    |

  4. In a town of 10000 families, it was found that 40% families buy ne...

    Text Solution

    |

  5. Complete solution set of inequlaity ((x+2)(x+3))/((x-2)(x-3))le1

    Text Solution

    |

  6. Integral value of x for, which (5x-1)lt(x+1)^2lt7x-3

    Text Solution

    |

  7. If set A ={x|(x^2(x-5)(2x-1))/((5x+1)(x+2)) lt 0 } and Set B={x|(3x...

    Text Solution

    |

  8. Number of intergers satisfying the inequality x^4- 29x^2+100 le 0 i...

    Text Solution

    |

  9. If n gt 0 and exactly 15 integers satisfying (x+6)(x-4 ) (x-5) (2x-...

    Text Solution

    |

  10. The solution of the inequality ((x+7)/(x-5)+(3x+1)/(2) )ge 0 is

    Text Solution

    |

  11. The complete solution set of inequality ((x-5)^(1005)(x+8)^(1008)(x-1)...

    Text Solution

    |

  12. Sum of solution of the equation |x|^3-4|x|^2+3|x|=0 is

    Text Solution

    |

  13. Number of integral roots of |x-1||x^2-2|=2 is

    Text Solution

    |

  14. The solution set of the inequlity (|x-2|-x)/(x)lt2 is

    Text Solution

    |

  15. Number of solutions of the equation |2-|x||=x +4 is a.0 b.1 c.2 d.Inf...

    Text Solution

    |

  16. Number of intergal values of x satisfying the inequality (x^2+6x-7)/(|...

    Text Solution

    |

  17. If -4lex lt 2 then ||x+2|-3| lies in the inerval

    Text Solution

    |

  18. Complete set of values of x satisfying inequality ||x-1|-5| lt 2x -5 ...

    Text Solution

    |

  19. If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then the set of values of x is

    Text Solution

    |

  20. The complete solution set of the equation |x^2-5x+6|+|x^2+12x+27|=|17x...

    Text Solution

    |