Home
Class 12
MATHS
IF a,b,c are real, show that the roots o...

IF a,b,c are real, show that the roots of each of the following equations are real:
` (x-a)(x-b)=b^2`

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5B(Multiple Choice type question)|5 Videos

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5B(Very short answer type question)|11 Videos

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5A(Short answer type question)|48 Videos

  • PROPERTIES OF TRIANGLE

    CHHAYA PUBLICATION|Exercise Assertion- Reason Type:|2 Videos

  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos

Similar Questions

Explore conceptually related problems

IF a,b, are real, show that the roots of each of the following equations are real: 1/(x-a)+1/(x-b)=1/a^2

IF a,b,c are real, show that the roots of each of the following equations are real: 1/(x-a)+1/(x-b)+1/(x-c)=0

IF a,b,c are real, show that the roots of each of the following equations are real: (b-c)x^2+2(c-a)x+a-b=0

Show that the roots of each of the following equations are rational(a,b,c are rational): (a-b+c)x^2+2cx+(b+c-a)=0

Show that the roots of each of the following equations are rational(a,b,c are rational): (b+c)x^2-(a+b+c)x+a=0

If a,b, are real, then show that the roots of the equation (x-a)(x-b) = b^2 are always real.

If a, b, c are real, then both the roots of the equation (x -b )(x -c)+(x -c)(x - a)+(x - a)(x - b)=0 are always

IF a,b,c are real, prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real and cannot be equal unless a=b=c.

IF c is real, show that the roots of the quadratic equation cx^2+(c-1)x+1-2c=0 are real. If the sum of the roots of the equation be equal to three times their difference, then find c.

Show that 1 is a root of a(b-c)x^(2)+b(c-a)x+c(a-b)=0 . Hence show that if roots of this equation are equal then (1)/(a),(1)/(b),(1)/(c) are in A.P

CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. IF alpha be a root of the quadratic equation 4x^2+2x-1=0, Let prove th...

    Text Solution

    |

  2. Letalpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta ...

    Text Solution

    |

  3. IF a,b,c are real, show that the roots of each of the following equati...

    Text Solution

    |

  4. IF a,b,c are real, show that the roots of each of the following equati...

    Text Solution

    |

  5. IF a,b, are real, show that the roots of each of the following equatio...

    Text Solution

    |

  6. IF a,b,c are real, show that the roots of each of the following equati...

    Text Solution

    |

  7. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show...

    Text Solution

    |

  8. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

  9. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

  10. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

  11. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

  12. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

  13. If the roots of the equation x^2+x+a=0 be real and unequal, then prove...

    Text Solution

    |

  14. Prove that, if the roots of the equation (a^2+b^2)x^2+2(bc+ad)x+(c^2+d...

    Text Solution

    |

  15. Show that the roots of the equation (a^4+b^4)x^2+4abcdx+(c^4+d^4)=0 ca...

    Text Solution

    |

  16. For what values of m the equations 3x^2+4mx+2=0 and 2x^2+3x-2=0 will h...

    Text Solution

    |

  17. Show that the equations px^2+qx+r=0 and qx^2+px+r=0 will have a common...

    Text Solution

    |

  18. If the two equations x^2+ax+b=0 and x^2+bx+a=0 (aneb) have a common ro...

    Text Solution

    |

  19. IF c is real, show that the roots of the quadratic equation cx^2+(c-1)...

    Text Solution

    |

  20. IF alpha is a root of the equation ax^2+bx+c=0 then show that malpha^2...

    Text Solution

    |