Home
Class 12
MATHS
If alpha,beta are the roots of the equat...

If `alpha,beta` are the roots of the equation `a x^2+b x+c=0,` then the value of `(aalpha^2+c)/(aalpha+b)+(abeta^2+c)/(abeta+b)` is a.`(b(b^2-2a c))/(4a)` b. `(b^2-4a c)/(2a)` c. `(b(b^2-2a c))/(a^2c)` d. none of these

A

`(b(b^(2) - 2ac))/(4a)`

B

`(b^(2) - 4ac)/(2a)`

C

`(b(b^(2) - 2ac))/(a^(2)c)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have `aalpha^(2) + c = -balpha` or `aalpha + b = -c/alpha`
Similarly, `abeta + b = -c/beta`
Hence, the given expression is
`b/c(alpha^(2) + beta^(2)) = (b(b^(2) - 2ac))/(a^(2)c)`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Linked Comprechension Type|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.13|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of the equation a x^2+b x+c=0 , then 1/(aalpha+b)+1/(abeta+b)= (a) c/(ab) (b) a/(bc) (c) b/(ac) (d) none of these

If alpha, beta are the roots of ax^(2) + bx + c = 0 then the equation with roots (1)/(aalpha+b), (1)/(abeta+b) is

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

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= (a) a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

If alpha,beta are the roots of the equation ax^2 + bx+c=0 then the roots of the equation (a + b + c)x^2-(b + 2c)x+c=0 are (a) c (b) d-c (c) 2c (d) 0

If alpha and beta are the zeros of the quadratic polynomial f(x)=a x^2+b x+c , then evaluate: (i) alpha^2beta+alphabeta^2 (ii) alpha^4+beta^4 (iii) 1/(aalpha+b)+1/(abeta+b)

If a and b are roots of the equation x^2+a x+b=0 , then a+b= (a) 1 (b) 2 (c) -2 (d) -1

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0 Then the roots of the equation (x-alpha)(x-beta)+c=0 are a ,c (b) b ,c a ,b (d) a+c ,b+c

If a,b and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .

CENGAGE ENGLISH-THEORY OF EQUATIONS-Single Correct Answer Type : Exercise
  1. Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), ...

    Text Solution

    |

  2. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

    Text Solution

    |

  3. If alpha,beta are the roots of the equation a x^2+b x+c=0, then the va...

    Text Solution

    |

  4. The quadratic x^2+a x=b+1=0 has roots which are positive integers, the...

    Text Solution

    |

  5. If alpha,beta re the roots of a x^2+c=b x , then the equation (a+c y)^...

    Text Solution

    |

  6. If alphaa n dbeta are roots of the equation a x^2+b x+c=0, then the ro...

    Text Solution

    |

  7. If the roots of the equation a x^2-b x+c=0a r ealpha,beta, then the ro...

    Text Solution

    |

  8. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  9. If alpha,beta are the nonzero roots of a x^2+b x+c=0a n dalpha^2,beta^...

    Text Solution

    |

  10. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)//ka n...

    Text Solution

    |

  11. If alpha, beta are the roots of ax^(2) + bx + c = 0 and alpha + h, bet...

    Text Solution

    |

  12. If one root of x^(2)-x-k=0 is square of the other, then find the value...

    Text Solution

    |

  13. If alpha and beta be the roots of the equation x^(2) + px - 1//(2p^(2)...

    Text Solution

    |

  14. If alpha,beta are the roots of x^2+p x+q=0 and gamma,delta are the roo...

    Text Solution

    |

  15. The value of m for which one of the roots of x^(2) - 3x + 2m = 0 is do...

    Text Solution

    |

  16. If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots an...

    Text Solution

    |

  17. If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equa...

    Text Solution

    |

  18. A quadratic equation with integral coefficients has two different prim...

    Text Solution

    |

  19. One of the roots of ax^(2) + bx + c = 0 is greater than 2 and the othe...

    Text Solution

    |

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

    Text Solution

    |