Home
Class 12
MATHS
The equation (a(x-b)(x-c))/((a-b)(a-c))...

The equation
`(a(x-b)(x-c))/((a-b)(a-c)) + (b(x-c)(x-a))/((b-c)(b-a))+ (c (x-a) (x-b))/((c-a)(c-b))= x ` is satisfied by

A

No value of x .

B

Exactly two values of x.

C

Exactly three values of x.

D

All values of x

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -C) (objective Type Questions ( more thena one options are correct )|35 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -D) Linked comprehension Type Questions|14 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos
  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos
  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x+b))/((a-c)(b-c))=1 is an identity.

The quadratic equation ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x+b))/((a-c)(b-c))=1 has (A) Two real and distinct roots (B) Two Equal roots (C) Non Real Complex Roots (D) Infinite roots

Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1 = (x^(3))/((x-a)(x-b)(x-c)) .

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

If (x^(4))/((x-a)(x-b)(x-c))= P(x)+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then P(x)=

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

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

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. if alpha&betaare the roots of the quadratic equation ax^2 + bx + c = 0...

    Text Solution

    |

  2. let alpha ,beta be roots of ax^2+bx+c=0 and gamma,delta be the roots o...

    Text Solution

    |

  3. The equation (a(x-b)(x-c))/((a-b)(a-c)) + (b(x-c)(x-a))/((b-c)(b-a))+...

    Text Solution

    |

  4. If z1=3−2i,z2=2−i and z3=2+5i then find z1+z2−3z3

    Text Solution

    |

  5. If the equation (k^(2)-3k +2) x^(2) + ( k^(2) -5k + 4)x + ( k^(2) -6k ...

    Text Solution

    |

  6. The value of k if

    Text Solution

    |

  7. if the difference of the roots of the equation x^(2)+ ax +b=0 is equa...

    Text Solution

    |

  8. If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then...

    Text Solution

    |

  9. If the equations ax^2 + bx + c = 0 and x^2 + x + 1= 0 has one common r...

    Text Solution

    |

  10. If 1,2,3 are the roots of the equation x^(3) + ax^(2) + bx + c=0 , th...

    Text Solution

    |

  11. Consider that f(x) =ax^(2) + bx +c, D = b^(2)-4ac , then which of the...

    Text Solution

    |

  12. If the minimum value ofx^2+2x+3 is m and maximum value of -x^2+4x+6 is...

    Text Solution

    |

  13. for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

    Text Solution

    |

  14. If one root of equation (l-m) x^2 + lx + 1 = 0 be double of the other ...

    Text Solution

    |

  15. if p,q,r are real numbers satisfying the condition p + q +r =0 , then ...

    Text Solution

    |

  16. The roots of the equation x^(3) -2x^(2) -x +2 =0 are

    Text Solution

    |

  17. IF alpha , beta are the roots of the equation x^2+2ax +b=0 , the...

    Text Solution

    |

  18. The set of all values of ' a ' for which the quadratic equation 3x^2+2...

    Text Solution

    |

  19. Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,the...

    Text Solution

    |

  20. If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2...

    Text Solution

    |