Home
Class 10
MATHS
Show that the roots of the quadratic equ...

Show that the roots of the quadratic equation:
`(b-c)x^2 + (c-a)x + (a-b) =0` are equal if c+a=2b.

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 12

    AGRAWAL PUBLICATION|Exercise EXERCISE|49 Videos

  • SAMPLE PAPER 4

    AGRAWAL PUBLICATION|Exercise EXERCISE|99 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

Show that the roots of the quadratic equation x^(2)-2(a+b)x+2(a^(2)+b^(2))=0 can not be real.

If the roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 are equal,show that 2/b=1/a+1/c.

Find the roots of quadratic equation ax^(2) + (a-b + c) x - b +c = 0 .

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

AGRAWAL PUBLICATION-Sample paper 13-EXERCISE
  1. If n is a positive odd integar, then show that n^2 - 1 is divisible by...

    Text Solution

    |

  2. Check whether 15^n can end with digit zero for any natural number n.

    Text Solution

    |

  3. Show that the roots of the quadratic equation: (b-c)x^2 + (c-a)x + (a...

    Text Solution

    |

  4. If P(5,7), Q(x,-2) and R(-3,y) are collinear points such that PR=2PQ, ...

    Text Solution

    |

  5. Prove that the diagonals of a rectangle with vertices (0,0), (a,0),(a,...

    Text Solution

    |

  6. Draw a line segment AB of length 7 cm . Locate a point R on AB such th...

    Text Solution

    |

  7. The sum of circumferences of two circles os 132 cm. If tha radius of o...

    Text Solution

    |

  8. In a car park, there are 125 cars, 3p otorbikes, 2q lorrie and 20 buse...

    Text Solution

    |

  9. Find the HCF and the LCM of 72 and 120 , using prime factorisation met...

    Text Solution

    |

  10. Express the length of a side of the n^(th) frame in terms of x and n.

    Text Solution

    |

  11. Find the value of x.

    Text Solution

    |

  12. A piece of wire is 99 cm long. It is cut bent into a frame in the sequ...

    Text Solution

    |

  13. If the roots of the equation x^2+2cx + ab +0 are real and unequal, pro...

    Text Solution

    |

  14. Let A(4,2), B(6,5) and C(1,4) be the verticles of triangleABC. The med...

    Text Solution

    |

  15. if tan theta = 12/13, evaluate (2 sin theta cos theta)/(cos^2 theta- s...

    Text Solution

    |

  16. If sec theta + tan theta = m, prove that (m^2 + 1)/(m^2- 1) = sin thet...

    Text Solution

    |

  17. A sphere of diameter 6 cm is dropped in a right circular cylinderical ...

    Text Solution

    |

  18. From the first floor of Qutab Minor, which is at a height of 25 m from...

    Text Solution

    |

  19. Prove that the line segments joining the mid-pointd of the sides of a ...

    Text Solution

    |

  20. A piece of cloth costs Rs. 35. If the piece were 4m longer and each me...

    Text Solution

    |