Home
Class 10
MATHS
Prove that the quadratic equation (a^2+b...

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`.

Promotional Banner

Topper's Solved these Questions

  • HINDU SCHOOL

    UNITED BOOK HOUSE|Exercise EXERCISE|54 Videos

  • HOWRAH ZILLA SCHOOL

    UNITED BOOK HOUSE|Exercise EXERCISE|55 Videos

Similar Questions

Explore conceptually related problems

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

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 .

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)

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.

The roots of the quadratic equation 2x^2+3x+1 =0 are

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.

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.

Find the roots of the quadratic equation |x^(2)|-3|x|+2=0 .

The roots of the quadratic equation x^(2)+a=0 are ______ .

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

UNITED BOOK HOUSE-HOOGHLY COLLIGIATE SCHOOL-EXERCISE
  1. A,B,C have started a partnership business by investing Rs 6,000 Rs 8,0...

    Text Solution

    |

  2. Joseph and Kuntal work in a factory. Joseph takes 5 minutes less time ...

    Text Solution

    |

  3. Prove that the quadratic equation (a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0 h...

    Text Solution

    |

  4. If x= (4sqrt(15))/(sqrt5+sqrt3), then (x+sqrt(20))/(x-sqrt(20))+(x+sqr...

    Text Solution

    |

  5. If x prop y and y prop z, then prove that : (x^2+y^2+z^2) prop (xy+yz+...

    Text Solution

    |

  6. If (x^2-yz)/a=(y^2-zx)/b=(z^2-xy)/c , show that (a+b+c)(x+y+z)=(ax+by...

    Text Solution

    |

  7. If b+c-a/x+y-x = c+a-b/c+x-y = a+bc/x+y-z, then prove that a/x = b/y =...

    Text Solution

    |

  8. State and Prove Pythagoras theorem.

    Text Solution

    |

  9. Answer any One queation : Prove that, if a perpendicular is draw on t...

    Text Solution

    |

  10. If in ABC,A is right angle and BP and CQ are two medians, then prove t...

    Text Solution

    |

  11. ABC is a triangle whose AB = AC. E is any point an extended BC, circum...

    Text Solution

    |

  12. Geometrically find the value of sqrt(29).

    Text Solution

    |

  13. Draw a right angled triangle length of hypotenuse and one of another s...

    Text Solution

    |

  14. In a circle, if an arc of 220 cm length subtends and angle of measure ...

    Text Solution

    |

  15. If sin theta+cos theta = 7/5 then sin theta cost theta = 12/25, find t...

    Text Solution

    |

  16. Find the value of (sin 25^@)/(sec65^@)+(cos 25^@)/(cosec 65^@).

    Text Solution

    |

  17. From a point on the roof a house 11 metres height, it is observed that...

    Text Solution

    |

  18. If the angle of depression of two consecutive km stones on a road fro...

    Text Solution

    |

  19. The length and breadth of a rectangular field of the village are 20m a...

    Text Solution

    |

  20. The external radius of a hollow sphere made of lead sheet of 1 cm thic...

    Text Solution

    |