Home
Class 12
MATHS
The real values of 'a' for which the qua...

The real values of 'a' for which the quadratic equation `2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0` possess roots of opposite sign is given by:

A

` a gt 5 `

B

`0 lt a lt 4 `

C

`a gt 0 `

D

`a gt 7`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Main ( Archive )|20 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos

  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

The value of 'a' for which the quadratic equation 2x^(2) - x(a^(2) + 8a -1) + a^(2) - 4a = 0 has roots with opposite signs, lie in the interval

The set of all values of ' a ' for which the quadratic equation 3x^2+2(a^2-3a+2)=0 possess roots of opposite sign, is a. (-oo,1) b. (-oo,0) c. (1,2) d. (3//2,2)

Write the value of k for which the quadratic equation x^2-k x+4=0 has equal roots.

The value of k for which the equation 3x^(2) + 2x (k^(2) + 1) + k^(2) - 3k + 2 = 0 has roots of opposite signs, lies in the interval

Write the set of values of k for which the quadratic equation has 2x^2+k x-8=0 has real roots.

Find the value of k for which the quadratic equation 3x^2+kx+3=0 has real and equal roots.

Is there any real value of ' a ' for which the equation x^2+2x+(a^2+1)=0 has real roots?

Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0 possesses at least two distinct positive roots

find the values k for which the quadratic equation 2x^2 + Kx +3=0 has two real equal roots

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -LEVEL -2
  1. The set off all values of m for which both the roots of the equation x...

    Text Solution

    |

  2. The equation x^(2) + ax + b^(2) = 0 has two roots each of which exceed...

    Text Solution

    |

  3. The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + ...

    Text Solution

    |

  4. if both root of equation x^2-6ax+2-2a+9a^2 = 0 exceeds 3 . then show t...

    Text Solution

    |

  5. If b gt a, then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a...

    Text Solution

    |

  6. which of the following graph represents the expression f(x) = ax^2 + b...

    Text Solution

    |

  7. If alpha, beta are the roots of the equation (x-a)(x-b)=c,c!=0. Find t...

    Text Solution

    |

  8. Let alpha ,beta " be the roots of " ax^(2) +bx + c= 0, gamma, detla ...

    Text Solution

    |

  9. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  10. If alpha , beta are roots of ax^(3) +bx +c=0 then the equation ax^...

    Text Solution

    |

  11. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  12. The polynomiaal (a x^2+b x+c)(a x^2-dx-c), a c!=0 has

    Text Solution

    |

  13. If the equation ax^(2)+2bx-3c=0 has no real roots and ((3c)/(4))lta+b,...

    Text Solution

    |

  14. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  15. If alpha and beta(alpha lt beta) are the roots of the equation x^(2)+b...

    Text Solution

    |

  16. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is

    Text Solution

    |

  17. If the roots of a1x^(2)+b1x+c1=0 and alpha1 , beta1 and those of a2...

    Text Solution

    |

  18. If b^2>4ac, then a(x^2 +4x+4)^2+b(x^2 +4x +4)+c=0 has distinct real ...

    Text Solution

    |

  19. If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R ,...

    Text Solution

    |

  20. The value of k for which the equation (k-2) x^(2) + 8x + k + 4 = 0 has...

    Text Solution

    |