Home
Class 12
MATHS
If the equation x ^(4)+kx ^(2) +k=0 has ...

If the equation `x ^(4)+kx ^(2) +k=0` has exactly two distinct real roots, then the smallest integral value of |k| is:

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

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 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

If the equation x^2+4x+k=0 has real and distinct roots, then (a) k 4 (c) kgeq4 (d) klt=4

If 5x^2-2kx+1 < 0 has exactly one integral solution which is 1 then sum of all positive integral values of k.

The equation kx^(2)+x+k=0 and kx^(2)+kx+1=0 have exactly one root in common for

Determine all real values of the parameter 'a' for which the equation 16x^4 - ax^3 + (2a + 17) x^2 - ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.

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 x^(2)-4x-(3k-1)|x-2|-2k+8=0,kinR , has exactly three distinct solutions, then k is equal to _____.

If the equation x^2-3kx+2e^(2logk)-1=0 has real roots such that the product of roots is 7 then the value of k is

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let p (x) be a polynomial with real coefficient and p (x)=x^(2)+2x+1. ...

    Text Solution

    |

  2. Find the smallest positive integral values of a for which the greater ...

    Text Solution

    |

  3. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

    Text Solution

    |

  4. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

    Text Solution

    |

  5. The number of integral value of a,a, in [-5, 5] for which the equation...

    Text Solution

    |

  6. The number of non-negative integral vlaues of n, n le 10 so that a roo...

    Text Solution

    |

  7. Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x...

    Text Solution

    |

  8. If x and y are real numbers connected by the equation 9x ^(2)+2xy+y^(2...

    Text Solution

    |

  9. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

    Text Solution

    |

  10. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

    Text Solution

    |

  11. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

    Text Solution

    |

  12. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

    Text Solution

    |

  13. Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+...

    Text Solution

    |

  14. The number of ordered pairs (a,b) where a,b are integers satisfying th...

    Text Solution

    |

  15. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

    Text Solution

    |

  16. If the range of the values of a for which the roots of the equation x ...

    Text Solution

    |

  17. Find the number of positive integers satisfying the inequality x^(2) -...

    Text Solution

    |

  18. If sin theta and cos theta are the roots of the quadratic equation ax...

    Text Solution

    |

  19. Let the inequality sin ^(2) x+a cos x +a ^(2) ge1+ cos x is satisfied...

    Text Solution

    |

  20. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

    Text Solution

    |