Home
Class 12
MATHS
In the equation x^2-px+q=0 one root is t...

In the equation `x^2-px+q=0` one root is twice of other then prove that `2p^2=9q`

Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 2|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 3|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

If the sum of the two roots of the quadratic equation x^2-px+q=0 be the thrice of their difference then prove that 2p^2=9q

In the equation x^2-px+q=0 ratio of the roots are 2:3 ,then prove that 6p^2=25q

If the sum of the roots of the equation x^2-px+q=0 be three times their difference show that, 2p^2=9q .

IF one root of the equation px^2+qx+r=0 is the cube of the other, prove that , rp(r+p)^2=(q^2-2rp)^2 .

In the equation px^2+rx+r=0 ratio of the roots are a:b then prove that p(a+b)^2=rab

If one root of the equation ax^2+bx+c=0 (a!=0) is twice the other, than show that 2b^2=9ac .

If one of the root of the equation px^2 + qx + r = 0 is the cube of the other, prove that. rp(r + p)^2 = (q^2 - 2rp)^2 .

If the ratio of the roots of the equation x^2-2px+q^2=0 be equal to the ratio of the roots of the equation x^2-2rx+s^2=0 , Prove that, p^2s^2=q^2r^2 .

If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal then prove that the roots of the equation (p + q)x^2 + 2qx + (p - q)=0 are imaginary,

If the difference of the roots of the quadratic equation x^(2)-px+q=0 be 1, then prove that p^(2)+4q^(2)=(1+2q)^(2) .

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
  1. In the equation x^2-px+q=0 one root is twice of other then prove that ...

    Text Solution

    |

  2. The inverse of the matrix [(1, 0,0),(a,1,0),(b,c,1)] is -

    Text Solution

    |

  3. If A=|a(ij)| and A(ij) denotes the cofactor of a(ij), then which of th...

    Text Solution

    |

  4. The minors of (-4) and 9 and the cofactors of (-4) and 9 in matrix [(...

    Text Solution

    |

  5. If |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

    Text Solution

    |

  6. If the system of equations x+y+z=6, x+2y+kz=0 and x+2y+3z=10 has no so...

    Text Solution

    |

  7. If A=[(-i,0),(0,i)] then A^(T)A is equal to -

    Text Solution

    |

  8. If A=[(0,3),(4,5)] and kA=[(0,4a),(3b,60)], then the values of k, a an...

    Text Solution

    |

  9. The value of the determinant |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)...

    Text Solution

    |

  10. If the matrix A stisfies the equation [(1,3),(0,1)]*A=[(1,1),(0,-1)],...

    Text Solution

    |

  11. For any matrix A, if A^(-1) exists then which of the following is not ...

    Text Solution

    |

  12. If a(1), a(2), a(3)…, a(n) are in G.P., then the value of the determin...

    Text Solution

    |

  13. The value of the determinant |((10)!,(11)!,(12)!),((11)!,(12)!,(13)!),...

    Text Solution

    |

  14. If C is the midpoint of AB and P is any point outside AB, then which o...

    Text Solution

    |

  15. The position vectors of the points A, B, C are (hati-3hatj-5hatk),(2h...

    Text Solution

    |

  16. If N be the set of natural numbers and and N(a)={an :n in N} then N(5)...

    Text Solution

    |

  17. If the function f: R to R is defined by f(x)=x^(2)-6x-14, then f^(-1)(...

    Text Solution

    |

  18. Let f:R to R be defined by f(x)=x^(2) and g:R to R be defined by g(...

    Text Solution

    |

  19. If f:R to S is defined by f(x)=sinx-sqrt(3)cosx+1 is onto, then the in...

    Text Solution

    |

  20. If (x^(3))/((2x-1) (x+2) (x-3))=A+ (B)/(2x-1) +(C )/(x+2) + (D)/(x-3),...

    Text Solution

    |

  21. The value of ["tan"^(-1)(m)/(n)-tan^(-1)((m-n)/(m+n))] is -

    Text Solution

    |