Home
Class 12
MATHS
If alpha and beta are the roots of the e...

If `alpha and beta` are the roots of the equation `ax ^(2) + bx + c=0,a,b, c in R , alpha ne 0` then which is (are) correct:

A

`alpha ^(2) +beta ^(2) =(b ^(2) -2ac)/(c ^(2))`

B

`(1)/(alpha^(2))+(1)/(beta^(2))=(b^(2) -2ac)/(c ^(2))`

C

`(1)/(alpha^(3))+(1)/(beta^(3))=(abc -b^(3))/(c ^(3))`

D

`alpha beta (alpha+beta ) =(-bc)/(alpha ^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 then log(a-bx+cx^(2)) is equal to

Two different real numbers alpha and beta are the roots of the quadratic equation ax ^(2) + c=0 a,c ne 0, then alpha ^(3) + beta ^(3) is:

If alpha,beta are the roots of the equation ax^2 + bx +c=0 such that beta < alpha < 0 , then the quadratic equation whose roots are |alpha|,|beta| is given by

If alpha beta( alpha lt beta) are two distinct roots of the equation. ax^(2)+bx+c=0 , then

If alpha and beta are the roots of the equation ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =

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

Let alpha and beta be the roots of the quadratic equation ax^(2)+bx+c=0, c ne 0, then form the quadratic equation whose roots are (1-alpha)/(alpha) and (1-beta)/(beta) .

If alpha, beta are the roots of the equation ax^(2) +2bx +c =0 and alpha +h, beta + h are the roots of the equation Ax^(2) +2Bx + C=0 then

If alpha, beta are the roots of the equation ax^2 + bx +c=0 then the value of (1+alpha+alpha^2)(1+beta+beta^2) is

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. Let f (x) =x ^(2) -4x +c AA x in R, where c is a real constant, then w...

    Text Solution

    |

  2. If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 +...

    Text Solution

    |

  3. If x satisfies |x-1| + |x-2|+|x-3|gt6, then : i)x ∈ (−∞,1) ii)x ∈...

    Text Solution

    |

  4. If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real ...

    Text Solution

    |

  5. If a,b are two numbers such that a ^(2) +b^(2) =7 and a ^(3) + b^(3) =...

    Text Solution

    |

  6. The number of non-negative integral ordered pair(s) (x,y) for which (x...

    Text Solution

    |

  7. If alpha, beta, gamma and delta are the roots of the equation x ^(4) -...

    Text Solution

    |

  8. The value of 'k' for which roots of the equation 4x^2-2x+k=0 are comp...

    Text Solution

    |

  9. If a,b,c in R, then for which of the following graphs of the quadrati...

    Text Solution

    |

  10. If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real ro...

    Text Solution

    |

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

    Text Solution

    |

  12. The equation cos ^(2) x - sin x+lamda = 0, x in (0, pi//2) has roots t...

    Text Solution

    |

  13. If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solutio...

    Text Solution

    |

  14. The number of non-negative integral ordered pair(s) (x,y) for which (x...

    Text Solution

    |

  15. If a lt 0, then the value of x satisfying x ^(2)-2a|x-a| -3a ^(2)=0 i...

    Text Solution

    |

  16. If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 +...

    Text Solution

    |

  17. Solve : | x - 1| + |x - 2| + | x - 3 | gt 6

    Text Solution

    |

  18. The value of 'k' for which roots of the equation 4x^2-2x+k=0 are comp...

    Text Solution

    |

  19. Let alpha , beta, gamma, delta are roots of x ^(4) -12x ^(3) +lamda x ...

    Text Solution

    |

  20. If the points ((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),(((b^2...

    Text Solution

    |