Home
Class 12
MATHS
if b^(2)ge4ac for the equation ax^(4)+b...

if `b^(2)ge4`ac for the equation `ax^(4)+bx^(2) +c=0` then roots of the equation will be real if

A

`bgt0,alt0,cgt0`

B

`blt0,agt0,cgt0`

C

`bgt0,agt0,cgt0`

D

`bgt0,alt0,clt0`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos
  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

Similar Questions

Explore conceptually related problems

If b^(2)ge4ac for the equation ax^(4)+bx^(2)+c=0 then all the roots of the equation will be real if

If a b c are distinct positive real numbers such that b(a+c)=2ac and given equation is ax^(2)+2bx+c=0 then the roots of the equation are ?

If a+b+c=0 then roots of the equation 3ax^(2)+4bx+5c=0 are

If coefficients of the equation ax^(2)+bx+c=0,a!=0 are real and roots of the equation are non-real complex and a+c

Let a,b and c be three real and distinct numbers.If the difference of the roots of the equation ax^(2)+bx-c=0 is 1, then roots of the equation ax^(2)-ax+c=0 are always (b!=0)

If a b c are distinct positive real numbers such that b(a+c)=2ac and given equation is ax^(2)+2bx+c=0 then (A) roots of given equation are imaginary (B) b is HM of a &c

If alpha and beta are the roots of the equation ax^(2)+bx+c=0, then what are the roots of the equation cx^(2) + bx + a = 0 ?

If b^(2)gt4ac then roots of equation ax^(4)+bx^(2)+c=0 are all real & distinct if :

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If the roots of the equation x^3-12 x^2+39 x-28=0 are in A.P. th...

    Text Solution

    |

  2. If P(x)=ax^2+bx+c, Q(x)=-ax^2+dx+c where ac!=0 then P(x).Q(x)=0 has

    Text Solution

    |

  3. if b^(2)ge4ac for the equation ax^(4)+bx^(2) +c=0 then roots of the e...

    Text Solution

    |

  4. The largest interval for whichx^(12)+x^9+x^4-x+1>0 -4<xlt=0 b. 0<x<1 ...

    Text Solution

    |

  5. IF a^2 + b^2 +c^2 =1 then the range of ab+bc +ca is

    Text Solution

    |

  6. The difference between the roots of the equation x^(2) + kx + 1=0 is ...

    Text Solution

    |

  7. The real value of a for which x^2+i(a-1)x+5=0 will have a pair of con...

    Text Solution

    |

  8. If a, b, c are positive then both roots of the equation ax^2 + bx+c=0

    Text Solution

    |

  9. The expression a^2x^2+bx+1 will be positive for all x in R if

    Text Solution

    |

  10. If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2...

    Text Solution

    |

  11. The least value of ax^2+bx+c,(a>0) is

    Text Solution

    |

  12. If x be real, then the maximum value of 5+4x-4x^2 will be equal to

    Text Solution

    |

  13. If x^2+p x=1 is a factor of the expression a x^3+b x=c , then a^2-c^2=...

    Text Solution

    |

  14. If a+b+c=0, then, the equation 3ax^(2)+2bx+c=0 has , in the interval ...

    Text Solution

    |

  15. If the value of ax^2+bx+c is always an integer for integral values of ...

    Text Solution

    |

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

    Text Solution

    |

  17. Fill in the blank : If f(x) = x+1/x , x in R Then the set of possible ...

    Text Solution

    |

  18. Fill in the blank : If 1+ i is a root of the equation ix^2-3x+p = 0 wh...

    Text Solution

    |

  19. Equation cos 2x+7=a(2-sin x) can have a real solution for

    Text Solution

    |

  20. If alpha,beta be the roots of x^2 - x-1 = 0 and An = alpha^n +beta^n, ...

    Text Solution

    |