Home
Class 12
MATHS
If the roots of the equation (b-c)x^2+(c...

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

Text Solution

AI Generated Solution

To determine the condition under which the roots of the equation \((b-c)x^2 + (c-a)x + (a-b) = 0\) are equal, we need to analyze the discriminant of the quadratic equation. ### Step-by-Step Solution: 1. **Identify the coefficients**: The given quadratic equation is in the form \(Ax^2 + Bx + C = 0\), where: - \(A = b - c\) - \(B = c - a\) ...
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|11 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|10 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

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

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

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

6.The roots of the equation (a-b+c)x^(2)+4(a-b)x+(a-b-c)=0 are

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

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//cdot

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

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

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

ARIHANT MATHS ENGLISH-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,...

    Text Solution

    |

  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

    Text Solution

    |

  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

    Text Solution

    |

  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

    Text Solution

    |

  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

    Text Solution

    |

  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

    Text Solution

    |

  7. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

    Text Solution

    |

  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

    Text Solution

    |

  9. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

    Text Solution

    |

  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

    Text Solution

    |

  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

    Text Solution

    |

  14. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

    Text Solution

    |

  17. The smallest value of k, for which both the roots of the equation, x^2...

    Text Solution

    |

  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

    Text Solution

    |

  20. solve 0=1+2x+3x^2

    Text Solution

    |

  21. Find the roots of x^2-6x-2=0

    Text Solution

    |