Home
Class 12
MATHS
If the equation x^4- λx^2+9=0 has fo...

If the equation x^4- λx^2+9=0 has four real and distinct roots, then `lamda` lies in the interval

A

`(-oo,-6)uu(6,oo)`

B

`(0,oo)`

C

`(6,oo)`

D

`(-oo,-6)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(4)-lamdax^(2)+9=0`
Let `x^(2)=tge0`
`:.f(t)=t^(2)-lamdat+9=0" "(1)`
If given equation has four real and distinct roods, then both roots of (1) must be positive
`:.Dgt0implieslamda^(2)-36gt0" "(2)`
`(-b)/(2a)gt0implies(lamda)/(2)gt0orlamdagt0" "(3)`
`f(0)gtor9gt0" "(4)`
`:.lambda in(-6,oo)" "["from(2),(3),(4)"]`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|43 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If the equation x^(2) + 4x - k = 0 has real and distinct roots, then

The equations x^(2) - 8x + k = 0 has real and distinct roots if :

If the equation x^(2)+4x+k=0 has real and distinct roots, then find the value of 'k'.

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

If both the roots of the quadratic equation x^(2) - mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval

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

If both the roots of the quadratic equation x^(2) mx+4=0 are real and distinct and they lie in the interval [1,5] then m lies in the interval

CENGAGE-THEORY OF EQUATIONS-Exercise (Comprehension)
  1. Consider the quadrationax^(2) - bx + c =0,a,b,c in N which has two di...

    Text Solution

    |

  2. Consider the inequation x^(2) + x + a - 9 lt 0 The values of the r...

    Text Solution

    |

  3. Consider the inequation x^(2) + x + a - 9 lt 0 The values of the re...

    Text Solution

    |

  4. Consider the inequation x^(2) + x + a - 9 lt 0 The value of the pa...

    Text Solution

    |

  5. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  6. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  7. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  8. (af(mu) lt 0) is the necessary and sufficient condition for a particu...

    Text Solution

    |

  9. (af(mu) lt 0) is the necessary and sufficient condition for a particu...

    Text Solution

    |

  10. (af(mu) lt 0) is the necessary and sufficient condition for a particu...

    Text Solution

    |

  11. Given |px^(2) + qx + r| le |Px^(2) + Qx + r|AA x in R and d=q^(2) - 4...

    Text Solution

    |

  12. If (x+2) is a common factor of (px^2+qx+r) and (qx^2+px+r) then a) ...

    Text Solution

    |

  13. Consider the equation x^4 + 2ax^3 + x^2 + 2ax + 1 = 0 where a in R. Al...

    Text Solution

    |

  14. Consider the equation x^4 + 2ax^3 + x^2 + 2ax + 1 = 0 where a in R. Al...

    Text Solution

    |

  15. Consider the equation x^4 + 2ax^3 + x^2 + 2ax + 1 = 0 where a in R. Al...

    Text Solution

    |

  16. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

    Text Solution

    |

  17. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

    Text Solution

    |

  18. If the equation x^4- λx^2+9=0 has four real and distinct roots, th...

    Text Solution

    |

  19. If the equation has no real root, then lamda lies in the interval

    Text Solution

    |

  20. If the equation x^4 -λx^2 +9 has only two real roods, then the set of ...

    Text Solution

    |