Home
Class 9
MATHS
If alpha and beta are the roots of 2x^(2...

If `alpha` and `beta` are the roots of `2x^(2) - x - 2 = 0`, then `(alpha^(3) + beta^(-3) + 2alpha^(-1) beta^(-1))` is equal to

A

`-(17)/(8)`

B

`(23)/(6)`

C

`(37)/(9)`

D

`-(29)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
() simplify the required expression and find `alpha + beta ` and `alphabeta`.
(ii) Find the sum of the roots and product of the roots.
(iii) Use relation, `a^(3) + b^(3) = (a+b)^(3) - 3ab(a+b)`.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 3|23 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 1|30 Videos

  • PROBABILITY

    PEARSON IIT JEE FOUNDATION|Exercise LEVEL 3|8 Videos

  • RATIO, PROPORTION AND VARIATION

    PEARSON IIT JEE FOUNDATION|Exercise Leval 3|10 Videos

Similar Questions

Explore conceptually related problems

If alpha ,beta, gamma are the roots of 2x^(3)-2x-1=0 then (sum alpha beta)^(2)

If alpha,beta and 1 are the roots of x^(3)-2x^(2)-5x+6=0 then (alpha,beta)=

If alpha and beta are the roots of 4x^(2) + 3x +7 =0 then the value of 1/alpha + 1/beta is

If alpha,beta are the roots of x^(2)+7x+3=0 ,then (alpha-1)^(2)+(beta-1)^(2)=

If alpha and beta are roots of the equaltion,3x^(2)-6x+15=0, then alpha^(3)beta^(2)+alpha^(2)beta^(3)

If alpha and beta are roots of the equation,3x^(2)-6x+15=0, then alpha^(3)beta^(2)+alpha^(2)beta^(3)=

If alpha and beta are the roots of x^(2) - (a+1)x + 1/2 (a^(2) + a+1) = 0 then alpha^(2) + beta^(2) = "_____" .

If alpha amd beta are the roots of the equation 3x^(2) - 2x - 8 = 0 then alpha^(2) + alpha beta + beta^(2) = "_____" .

If alpha and beta are the roots of the equation 4x^(2)+3x+7=0, then (1)/(alpha)+(1)/(beta)=

PEARSON IIT JEE FOUNDATION-QUADRATIC EXPRESSIONS AND EQUATIONS-Level 2
  1. If one of the roots of x^2+(1+k)x+2k=0 is twice the other, then (a^2+b...

    Text Solution

    |

  2. If alpha and beta are the roots of 2x^(2) - x - 2 = 0, then (alpha^(3...

    Text Solution

    |

  3. In a right angled triangle one of the perpendicular sides is 4 cm grea...

    Text Solution

    |

  4. In a friction, the denominator is 1 less than the numerator. The sum o...

    Text Solution

    |

  5. The length of the rectangular surface of a table is 10m more than its ...

    Text Solution

    |

  6. If alpha and beta the roots of the equation x^(2) + 9x + 18 = 0, then ...

    Text Solution

    |

  7. Find the minimum value of the quadratic expression 4x^(2) -3x + 4.

    Text Solution

    |

  8. If (x+2) is a common factor of the expression x^(2) + ax - 6, x^(2) +...

    Text Solution

    |

  9. The roots of a pure quadratic equation exists only if "".

    Text Solution

    |

  10. The root of the equation (x-1)/(x-2) + (x-3)/(x-4) = 2'1/3. (where a...

    Text Solution

    |

  11. If x+3 is the common factor of the expreassions ax^(2) + bx + 1 and px...

    Text Solution

    |

  12. If the sum of the roots of an equation x^(2) + px + 1 = 0(p gt 0) is ...

    Text Solution

    |

  13. The equation x + 5/(3-x) = 3 + (5)/(3-x) has

    Text Solution

    |

  14. The roots of the equation (1)/(2x-3) - (1)/(2x+5) = 8 are

    Text Solution

    |

  15. If the quadratic expression x^(2) + (a-4)x + (a+4) is a perfect square...

    Text Solution

    |

  16. The minimum value of 2x^(2) - 3x+ 2 is "".

    Text Solution

    |

  17. The roots of x^(2) - 2x-1= 0 are "".

    Text Solution

    |

  18. if 2x^(2) + 4x - k = 0 is same as (x-5) (x+k/10) = 0, then find the ...

    Text Solution

    |

  19. If the numerically smaller root of x^(2) + mx = 2 is 3 more than the o...

    Text Solution

    |