Home
Class 10
MATHS
If the roots of the quadratic equation (...

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.

Promotional Banner

Topper's Solved these Questions

  • Application of Trigonnometric Ratios : Heights of Distance

    UNITED BOOK HOUSE|Exercise Exercise |29 Videos

Similar Questions

Explore conceptually related problems

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.

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

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 (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 equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

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

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)

Show that the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal if a,b,c are in H.P.

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

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

UNITED BOOK HOUSE-ANISHMALI UNTIED ACADEMY-EXERCISE
  1. Find the sum of money if the difference between compound interest and ...

    Text Solution

    |

  2. Dipu, Rabeya and Megha have started a small business by investing that...

    Text Solution

    |

  3. If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are eq...

    Text Solution

    |

  4. Solve: 1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6[x!=1,2,3,4]

    Text Solution

    |

  5. If x= (sqrt7+sqrt3)/(sqrt7-sqrt3) and xy= 1 then find the value of (x^...

    Text Solution

    |

  6. If (x^3+y^3) alpha(x^3-y^3) prove that (x^2+y^2) alpha(x^2-y^2).

    Text Solution

    |

  7. If a,b,c, are in continued proportion then prove that a^2b^2c^2(1/a^3+...

    Text Solution

    |

  8. If x/y= (a+2)/(a-2) show that (x^2-y^2)/(x^2+y^2)=(4a)/(a^2+4)

    Text Solution

    |

  9. Prove that opposite angles of a cyclic quadrilateral are supplementary

    Text Solution

    |

  10. State and Prove Pythagoras theorem.

    Text Solution

    |

  11. Prove that cyclic trapezium is isoscles trapezium and the length of it...

    Text Solution

    |

  12. O is any point inside a rectangle. Prove that OA^2+OC^2=OB^2+OD^2.

    Text Solution

    |

  13. Answer any one question : Draw an equilateral triangle of side of 6 c...

    Text Solution

    |

  14. Geometrically find the value of sqrt(9 ).

    Text Solution

    |

  15. If tan theta = a/b then find the simpliest value of (b cos theta-a sin...

    Text Solution

    |

  16. Prove that (2tan^2 (30^@))/(1-tan^2(30^@))+sec^2(45^@)-cot^2(45^@) = s...

    Text Solution

    |

  17. Show that cosec^2(25^@)cot^2(65^@)=sin^2(25^@)+sin^2(65^@)+cot^2(65^@...

    Text Solution

    |

  18. The height of 2nd tower is equal to 1/3rd the height of 1st tower. The...

    Text Solution

    |

  19. If the angle of elevation of the top and Monument when observed from a...

    Text Solution

    |

  20. Total surface area of a right circular pot open at one end is 2002 sq....

    Text Solution

    |