Home
Class 11
MATHS
Let alpha1,beta1 be the roots x^2-6x+p=0...

Let `alpha_1,beta_1` be the roots `x^2-6x+p=0a n d` `alpha_2,beta_2` be the roots `x^2-54 x+q=0dot` If `alpha_1,beta_1,alpha_2,beta_2` form an increasing G.P., then sum of the digits of the value of `(q-p)` is ___________.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the roots of x^2-4x+q=0 . If alpha,beta,gamma are in GP , then the integer values of p and q respectively are:

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.

Let alpha,beta be the roots of x^(2)-x-1=0ands_(n)=alpha^(n)+beta^(n) for all integers nge1 . Then for every integer nge2 -

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are (alpha+1//beta)a n d(beta+1//alpha) .

Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 and delta=b^2-4a cdot If alpha+beta,alpha^2+beta^2alpha^3+beta^3 are in G.P. Then a. =0 b. !=0 c. b =0 d. c =0

Let alpha,beta be the roots of x^(2)-2xcosphi+1=0 , then the equation whose roots are alpha^(n),beta^(n) is

If alpha,beta are the roots of x^2-px+1=0 and gamma is a root of x^2+px+1=0 , then (alpha+gamma)(beta+gamma) is

If the roots of equation 5x^2-3x+6=0 are alpha and beta then find the value of 1/alpha+1/beta

Let alpha, beta be the roots of the equation x^(2)-6x-2=0 with alpha gt beta . If a_(n)=alpha^(n)-beta^(n) for n ge 1 , then the value of (a_(10)-2a_(8))/(2a_(9)) is

Let alpha,beta be the roots of x^2-x-1=0 and S_n=alpha^n+beta^n , for all integers nge1 . Then for every integer nge2 ,

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Polynomial P(x) contains only terms of odd degree. when P(x) is divide...

    Text Solution

    |

  2. If the equation 2x^2+4x y+7y^2-12 x-2y+t=0, where t is a parameter has...

    Text Solution

    |

  3. Let alpha1,beta1 be the roots x^2-6x+p=0a n d alpha2,beta2 be the root...

    Text Solution

    |

  4. If sqrt(sqrt(sqrt(x)))=(3x^4+4)^(1/64), then the value of x^4 is.

    Text Solution

    |

  5. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8...

    Text Solution

    |

  6. If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negati...

    Text Solution

    |

  7. Given alphaa n dbeta are the roots of the quadratic equation x^2-4x+k...

    Text Solution

    |

  8. If (x^2+a x+3)/(x^2+x+a) takes all real values for possible real value...

    Text Solution

    |

  9. If cos^4theta+alpha and sin^4theta+alpha are the roots of the equation...

    Text Solution

    |

  10. If the roots of the equation x^2+a x+b=0 are c and d , then roots of ...

    Text Solution

    |

  11. If a ,b ,c in R a n d a b c&lt;0 , then equation b c x^2+(2b+c-a)x+a...

    Text Solution

    |

  12. For the quadratic equation x^2+2(a+1)x+9a-5=0, which of the following ...

    Text Solution

    |

  13. Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor ...

    Text Solution

    |

  14. If |a x^2+b x+c|lt=1 for all x in [0, 1], then a.|a|lt=8 b. |b|>8 ...

    Text Solution

    |

  15. Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c<0...

    Text Solution

    |

  16. If roots of a x^2+b x+c=0 are alphaa n dbetaa n d4a+2b+c >0,4a -2b+c >...

    Text Solution

    |

  17. The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has

    Text Solution

    |

  18. Find the complete set of values of a such that (x^2-x)/(1-a x) atta...

    Text Solution

    |

  19. If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots o...

    Text Solution

    |

  20. If he roots of the equation12 x^2-m x+5=0 are in the ratio 2:3 then fi...

    Text Solution

    |