Home
Class 12
MATHS
If the equation x^(2)-4x-(3k-1)|x-2|-2k+...

If the equation `x^(2)-4x-(3k-1)|x-2|-2k+8=0,kinR`, has exaclty three distinct solutions, then k is eaual to _____.

Text Solution

Verified by Experts

The correct Answer is:
2
Given equation is
`(x-2)^(2)-4-(3k-1)|x-2|-2k+8=0` or
`r^(2)-(3k-1)t-2k+4=0`, where `t=|x-2|`
For exactly 3 distinct solutions, one of the roots is zero and other root is positive.
`:.k=2`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Main Previous Year|7 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

If the equation 4x^(3)+5x+k=0(k in R) has a negative real root then

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

If the equation 2x^2+k x y+2y^2=0 represents a pair of real and distinct lines, then find the values of kdot

Minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solution,

If k be an integer and p is a prime such that the quadratic equation x^(2)+k x+p=0 has two distinct positive integer solutions find the value of -(k+p) .

If the equation x^(3)+k x^(2)+3=0 and x^(2)+k x+3=0 have a common root, then the value k .

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is three (b) two (c) infinitely many (d) zero

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1

CENGAGE-THEORY OF EQUATIONS-Exercise (Numerical)
  1. Given that x^2-3x+1=0, then the value of the expression y=x^9+x^7+x^(-...

    Text Solution

    |

  2. If sin^(2)alpha,cos^(2)alphaand-cosec^(2)alpha are the zeros of P(x)=x...

    Text Solution

    |

  3. If the equation x^(2)-4x-(3k-1)|x-2|-2k+8=0,kinR, has exaclty three di...

    Text Solution

    |

  4. Statement 1 : If cos^2\ pi/8 is a root of the equation x^2+ax+b=0, whe...

    Text Solution

    |

  5. Given alphaa n dbeta are the roots of the quadratic equation x^2-4x+k=...

    Text Solution

    |

  6. Let alpha1,beta1 be the roots x^2-6x+p=0a n d alpha2,beta2 be the root...

    Text Solution

    |

  7. Let alphaa n dbeta be the solutions of the quadratic equation x 62-115...

    Text Solution

    |

  8. The quadratic equation x^2+m x+n=0 has roots which are twice those of ...

    Text Solution

    |

  9. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

    Text Solution

    |

  10. Polynomial P(x) is divided by (x-3) , the remainder if 6.If P(x) is di...

    Text Solution

    |

  11. If alphaandbeta are the roots of the equation x^(2)-6x+12=0 and the va...

    Text Solution

    |

  12. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

    Text Solution

    |

  13. Let a,binRandabne1."If "6a^(2)+20a+15=0and15b^(2)+20b+6=0 then the va...

    Text Solution

    |

  14. If there exists at least one real x which satisfies both the equatios ...

    Text Solution

    |

  15. If the equation x^(2)+2(lamda+1)x+lamda^(2)+lamda+7=0 has only negativ...

    Text Solution

    |

  16. All he value of k for which the quadratic polynomial f(x)=2x^2+k x+k^2...

    Text Solution

    |

  17. If set of values a for which f(x)=a x^2-(3+2a)x+6a!=0 is positive for ...

    Text Solution

    |

  18. a ,b ,a n dc are all different and non-zero real numbers on arithmetic...

    Text Solution

    |

  19. Let P(x)=5/4+6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniqu...

    Text Solution

    |

  20. If equation x^4-(3m+2)x^2+m^2=0(m >0) has four real solutions which ar...

    Text Solution

    |