Home
Class 11
MATHS
If,alpha be the root of equation ax^2+bx...

If,`alpha` be the root of equation `ax^2+bx+c=0` and `beta` be root of `-ax^2+bx+c=0` then prove that there will be a root of the equation `ax^2+2bx+2c=0` lying between `alpha` and `beta`, where a and c are non zero.

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

The roots of the equation ax^2+bx+c=0 are equal when-

One root of the equation ax^2+bx+c=0(ane0) is zero when-

IF a,b,c are in G.P prove that the roots of the equation ax^2+2bx+c=0 are equal.

If the roots of the equation ax^2+bx+c=0(a!=0) be equal then

If the roots of the equation ax^(2)+bx+c=0(ane0) be equal, then

IF b=c=0 then both roots of the equation ax^2+bx+c=0(ane0) are-

If a, b, c are in arithmetic progression, then the roots of the equation ax^2-2bx+c=0 are

IF a=0 and b=0 then both roots of the equation ax^2+bx+c=0 are-

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

If the two roots of the equation ax^2 + bx + c = 0 are distinct and real then

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. f(x)=x^2-(m-3)x+m=0 is a quadratic equation, find values of m for whic...

    Text Solution

    |

  2. f(x)=x^2-(m-3)x+m=0 is a quadratic equation, find values of m for whic...

    Text Solution

    |

  3. If,alpha be the root of equation ax^2+bx+c=0 and beta be root of -ax^2...

    Text Solution

    |

  4. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

    Text Solution

    |

  5. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

    Text Solution

    |

  6. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has No...

    Text Solution

    |

  7. For what value of 'm' inR, both roots of the equation x^2-6mx+9m^2-2m+...

    Text Solution

    |

  8. Find the value(s) of 'a' for which the inequality tan^(2)x+(a+1) t...

    Text Solution

    |

  9. Find the common root of x^2-3x+2=0 and x^2+x-2=0

    Text Solution

    |

  10. Find the condition if equations ax^2+bx+c=0 and x^2+2x+3=0 have a comm...

    Text Solution

    |

  11. If x^2+ax+bc=0 and x^2+bx+ac=0 have a common root, show their other ro...

    Text Solution

    |

  12. If alpha,beta are the roots x^2+px+q=0 and gamma,delta are the roots o...

    Text Solution

    |

  13. Find condition if ax^3+bx^2+cx+d=0, has exactly one real root, (a,b,c,...

    Text Solution

    |

  14. Let P(x)equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c))....

    Text Solution

    |

  15. Solve the equation (x^2-6x)^2=81+2(x-3)^2

    Text Solution

    |

  16. Show f(x)=x^3+px+q=0 has a repeated root if 4p^3+27q^2=0

    Text Solution

    |

  17. Show x^5-2x^2+7=0 has atleast two imaginary roots.

    Text Solution

    |

  18. Solution set of x satisfying abs(x/(x-1))+absx=x^2/abs(x-1) is

    Text Solution

    |

  19. Solve the equation abs(x-abs(4-x))-2x=4

    Text Solution

    |

  20. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

    Text Solution

    |