Home
Class 10
MATHS
If the roots of the equation x^2+2c x+a ...

If the roots of the equation `x^2+2c x+a b=0` are real unequal, prove that the equation `x^2-2(a+b)x+a^2+b^2+2c^2=0` has no real roots.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|183 Videos

  • REAL NUMBERS

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

If the roots of the equation , x^2+2c x+ab=0 are real and unequal, then the roots of the equation, x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: a. real and unequal b. real and equal c. imaginary d. Rational

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If roots of equation x^3-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

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

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

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

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

Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no real root, if a d!=b c .

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

RD SHARMA ENGLISH-QUADRATIC EQUATIONS-All Questions
  1. Find the roots of the quadratic equations (if they exist) by the metho...

    Text Solution

    |

  2. Find the roots of the quadratic equations (if they exist) by the metho...

    Text Solution

    |

  3. If the roots of the equation x^2+2c x+a b=0 are real unequal, prove th...

    Text Solution

    |

  4. If p , q , ra n ds are real numbers such that p r=2(q+s), then show th...

    Text Solution

    |

  5. Find the values of k for which the equation x^2+5k x+16=0 has no real ...

    Text Solution

    |

  6. If p ,q are real p!=q , then show that the roots of the equation (p-q)...

    Text Solution

    |

  7. If-4 is a root of the quadratic equation x^2+p x-4=0 and the quadratic...

    Text Solution

    |

  8. Find the values of k for which the following equation has equal roots:...

    Text Solution

    |

  9. Find the value of k for which the given equation has real and equal ro...

    Text Solution

    |

  10. Determine the nature of the roots of the following quadratic equations...

    Text Solution

    |

  11. Using quadratic formula, solve the following equation for x: a b x^2+...

    Text Solution

    |

  12. Using quadratic formula solve the following quadratic equations: p^2x^...

    Text Solution

    |

  13. Solve the following quadratic equations by factorization method: (x+3...

    Text Solution

    |

  14. Solve the following quadratic equations by factorization method: ...

    Text Solution

    |

  15. Which of the following are quadratic equations? (i)x^2-6x+4=0 (i...

    Text Solution

    |

  16. Which of the following are quadratic equations? (i)x+3/x=x^2 (ii...

    Text Solution

    |

  17. Which of the following are quadratic equations? x^2+2sqrt(x)-3=0 (ii...

    Text Solution

    |

  18. In each of the following determine whether the given values are solu...

    Text Solution

    |

  19. In each of the following determine whether the given values are solu...

    Text Solution

    |

  20. In each of the following, determine the value of k for which the g...

    Text Solution

    |