Home
Class 12
MATHS
Prove that, if the roots of the equation...

Prove that, if the roots of the equation `(a^2+b^2)x^2+2(bc+ad)x+(c^2+d^2)=0` be real, then they are equal.

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

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)(x-c)=0 are real.

If the roots of the quadratic equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 are equal, prove that a/b=c/d .

Prove that the quadratic equation (a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0 has no real roots when ad!=bc .

If the roots of the quadratic equation (a^(2)+b^(2))x^(2)-2(ac+bd)x+(c^(2)+d^(2))=0 be equal then prove that (a)/(b)=(c)/(d)

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 are equal if either b=0 or , a^3+b^3+c^3-3abc=0

CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. Find the condition that the roots of the quadratic equation x^2+px+q=0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. If the quadratic equations x^2+ax+b=0 and x^2+bx+a=0(aneb) have a comm...

    Text Solution

    |

  11. If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of...

    Text Solution

    |

  12. If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5...

    Text Solution

    |

  13. If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5...

    Text Solution

    |

  14. IF x is real , find the greatest and the least value of : (x^2+14x+9...

    Text Solution

    |

  15. IF x is real , find the greatest and the least value of : (x^2-2x+2)...

    Text Solution

    |

  16. Show that for all real values of x the value of (x^2-3x+4)/(x^2+3x+4) ...

    Text Solution

    |

  17. If x is real, show that the value of x/(x^2-5x+9) always lie between 1...

    Text Solution

    |

  18. If x is real show that the expressions (x^2+34x-71)/(x^2+2x-7) has no ...

    Text Solution

    |

  19. If x is real show that the expressions ((x-1)(x+3))/((x-2)(x+4)) has n...

    Text Solution

    |

  20. If x is real then the expressions (x^2+2x-11)/(x-3) assumes those valu...

    Text Solution

    |