Home
Class 12
MATHS
Let alpha, beta are two real roots of eq...

Let `alpha, beta` are two real roots of equation `x ^(2) + px+ q =0, p ,q, in R, q ne 0.` If the quadratic equation `g (x) =0` has two roots `alpha + (1)/(alpha) , beta + (1)/(beta)` such that sum of its roots is equal to product of roots, then number of integral values g can attain is :

A

`[(1)/(3), 3]`

B

`((1)/(3), 3]`

C

`[(1()/(3), 3)`

D

`(-oo, (1)/(3))uu [3,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • QUADRATIC EQUATIONS

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

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

If tan alpha tan beta are the roots of the equation x^2 + px +q =0(p!=0) then

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

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

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) .

The roots of the equation ax^(2)+bx+c=0 are alpha and beta . Form the quadratic equation whose roots are alpha+(1)/(beta) and beta+(1)/(alpha) .

If alphaandbeta be the roots of the quadratic equation x^(2)+px+q=0 , then find the quadratic equation whose roots are (alpha-beta)^(2)and(alpha+beta)^(2) .

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 are the roots of the equation ax^2+ bx +c=0 then the quadratic equation whose roots are alpha + beta , alpha beta is

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let alpha, beta are two real roots of equation x ^(2) + px+ q =0, p ,q...

    Text Solution

    |

  2. Let f (x) =ax ^(2) + bx+ c where a,b,c are integers. If sin ""pi/7. si...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

    Text Solution

    |

  5. The number of positive integral values of , m le 16 for which the equa...

    Text Solution

    |

  6. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x ^(2) + 17 x +7 is perfect square ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

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

    Text Solution

    |

  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |