Home
Class 11
MATHS
If he equation x^3+a x^2+b x+216=0 has t...

If he equation `x^3+a x^2+b x+216=0` has three real roots in G.P., then `b//a` has the value equal to _____.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If the equation x^(2)+y^(2)-10x+21=0 has real roots x=alphaandy=beta then

If a and b are positive numbers and eah of the equations x^2+a x+2b=0 and x^2+2b x+a=0 has real roots, then the smallest possible value of (a+b) is_________.

If the equation x^4 -λx^2 +9=0 has only two real roots, then the set of values of λ is

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

If the equation 2x^(4)+x^(3)-2x-1=0 has two real roots alpha and beta , then between alpha and beta the equation 8x^(3)+3x^(2)-2=0 has -

If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consecutive positive integers, then the value of (a^2//(b+1)) is equal to?

Find the value of a if x^3-3x+a=0 has three distinct real roots.

Find the value of k if x^3-12x+k=0 has three real distinct roots.

Show that the equation e^(x-1)+x-2=0 has no real root greater than 1.

Show that the equation e^(x-1)+x-2=0 has no real root which is less than 1.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  2. If the sixth term of an H.P. is 10 and the 11th term is 18 Find the 16...

    Text Solution

    |

  3. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

    Text Solution

    |

  4. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

    Text Solution

    |

  5. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

    Text Solution

    |

  6. For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) th...

    Text Solution

    |

  7. If x >1,y >1,a n dz >1 are in G.P., then 1/(1+lnx),1/(1+l ny)a n d1/(1...

    Text Solution

    |

  8. Compute the 100th term of HP if the 10th and 20th term of HP are 20 an...

    Text Solution

    |

  9. Find the 6th and nth term of the GP 2, 6, 18, 54,.....

    Text Solution

    |

  10. If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

    Text Solution

    |

  11. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

    Text Solution

    |

  12. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

    Text Solution

    |

  13. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P...

    Text Solution

    |

  14. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

    Text Solution

    |

  15. The geometric mean between -9 and -16 is a.12 b. -12 c. -13 d. none of...

    Text Solution

    |

  16. The value of 0.568 x 4.9 =?

    Text Solution

    |

  17. If (1+x)(1+x^2)(1+x^4)....(1+x^128)=sum(r=0)^nx^r then n is

    Text Solution

    |

  18. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

    Text Solution

    |

  19. Express the given complex number in (a+ib) form: (5-2i)^2

    Text Solution

    |

  20. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

    Text Solution

    |