Home
Class 12
MATHS
Prove that (ax^(2))/((x -a)(x-b)(x-c))...

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))`.

Text Solution

Verified by Experts

`(ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1`
`=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x -b)(x-c))+((c +x-c)/(x-c))`
`=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(x)/(x-c)`
`=(ax^(2))/((x-a)(x-b)(x-c))+(bx +x(x-b))/((x-b)(x-c))`
`=(ax^(2))/((x-a)(x-b)(x-c))+(x^(2))/((x-b)(x-c))`
`=(ax^(2)+x^(2)(x-a))/((x-a)(x-b)(x-c))`
`=(x^(3))/((x-a)(x-b)(x-c))`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 then (y')/(y)=

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 find (dy)/(dx)

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

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 then prove that (y')/(y)=(1)/(x)[(a)/(a-x)+(b)/(b-x)+(c)/(c-x)]

Prove that (x^(b-c))^(a)(x^(a-b))^(c)(x^(c-a))^(b)=1

(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)/(a/(x-a)+b/(x-b)+c/(x-c))

Prove that :((x^(a))/(x^(b)))^(a+b-c)((x^(b))/(x^(c)))^(b+c-a)((x^(c))/(x^(a)))^(c+a-b)=1

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

Prove that: ((x^(a))/(x^(b)))^(c)x((x^(b))/(x^(c)))^(a)x((x^(c))/(x^(a)))^(b)=1

CENGAGE-THEORY OF EQUATIONS-Examples
  1. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

    Text Solution

    |

  2. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the remainder when x^2+4x^2-7x+6 is diided by x-1.

    Text Solution

    |

  5. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

    Text Solution

    |

  6. Let a ne 0 and P(x) be a polynomial of degree greater then 2.If P(x) l...

    Text Solution

    |

  7. Given that x^2+x-6 is a factor of 2x^4+x^3+b x+a+b-1, find the value o...

    Text Solution

    |

  8. Use the factor theorem to find the value of k for which (a+2b),w h e r...

    Text Solution

    |

  9. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

    Text Solution

    |

  10. Let f(x)= x^(3) + x + 1 and P(x) be a cubic polynomial such that P(0) ...

    Text Solution

    |

  11. Let f(x) be a polynomial with integral coefficients. If f(1) and f(2)...

    Text Solution

    |

  12. Let a ,b in na n a > 1. Also p is a prime number. If a x^2+b x+c=p fo...

    Text Solution

    |

  13. What is Identity equation & Inequalities ? (i)If (a^2-1)x^2+(a-1)x+a^2...

    Text Solution

    |

  14. Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x...

    Text Solution

    |

  15. A certain polynomial P(x)x in R when divided by kx-a ,x-ba n dx-c lea...

    Text Solution

    |

  16. If alpha, beta, gamma are such that alpha+beta+gamma=2, alpha^2+beta^2...

    Text Solution

    |

  17. If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(x)+(1)/...

    Text Solution

    |

  18. In how many points graph of y=x^3-3x2+5x-3 interest the x-axis?

    Text Solution

    |

  19. Consider the following figure. Answer the following questions (...

    Text Solution

    |

  20. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

    Text Solution

    |