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

If `alpha , beta ` are the roots of the quadratic equation ` (p^2 + p + 1) x^2 + (p - 1) x + p^2 = 0 ` such that unity lies between the roots then the set of values of ` p ` is (i) `O/` (ii) `p in (-infty,-1) cup (0,infty)` (iii) `p in (-1,infty)` (iv) `(-1,1)`

Text Solution

Verified by Experts

The correct Answer is:
`p in(-1,0)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of the quadratic equation (p^(2)+p+1)x^(2)+(p-1)x+p^(2)=0 such that unity lies between the roots then the set of values of p is (i) 0 (ii) p in(-oo,-1)uu(0,oo)( iii) p in(-1,oo) (iv) (-1,1)

If 1 - p is a root of the quadratic equation x^(2) + px + 1- p = 0 , then its roots are

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

1.Find the roots of the equation x^(2)+x-p(p+1)=0

If the roots of the quadratic equation 3x^(2)+5x+3(4p-1)=0 is reciprocal of each other. Find the value of p

Let alpha and beta be the roots of a quadratic equation 4x^(2)-(5p+1)x+5p=0. If beta=1+alpha, then the integral value of p, is

RESONANCE-DPP-QUESTION
  1. If every pair from among the equations x^2+px+qr=0,x^2+qx+rp=0 and x...

    Text Solution

    |

  2. Find a and b so that x^3+ax^2+11x+6 and x^3+bx^2+14x+8 may have one co...

    Text Solution

    |

  3. If alpha , beta are the roots of the quadratic equation (p^2 + p +...

    Text Solution

    |

  4. The roots alpha and beta of a quadratic equation are the square of two...

    Text Solution

    |

  5. The number of values of x in the interval [0, 5pi] satisfying the equa...

    Text Solution

    |

  6. If 2cos^2(pi+x)+3 sin(pi+x) vanishes then the values of x lying in the...

    Text Solution

    |

  7. ax^2+2bx-3c=0 has no real root and a+bgt3c/4 then

    Text Solution

    |

  8. The value of the expression ((sin3theta)/sin theta)^2-((cos3theta)/cos...

    Text Solution

    |

  9. Find the smallest positive integral value of a for which the greater r...

    Text Solution

    |

  10. The set of values of 'c' for which the equation x^(2)-4x-c-sqrt(8x^(2)...

    Text Solution

    |

  11. Let the equations x^(3)+2x^(2)+px+q=0and x^(3)+x^(2)+px+r=0 have two t...

    Text Solution

    |

  12. If lta(n)gtandltb(n)gt be two sequences given by a(n)=(x)^((1)/(2^(n))...

    Text Solution

    |

  13. Sum of all the solutions of the equation : tan^2 33x = cos2x - 1 which...

    Text Solution

    |

  14. Consider the cubic equation x^3-x^2+(x-x^2) sin theta +(x-x^2) cos the...

    Text Solution

    |

  15. Consider the equation, sin^4 x-cos^2 x sin x + 2 sina^2 x + sin x = 0 ...

    Text Solution

    |

  16. If sintheta+sinphi=aand costheta+cosphi =b, then

    Text Solution

    |

  17. If sin theta+cos theta=1/5and 0ltthetalt2pi,then tan thetais

    Text Solution

    |

  18. lf sin(x-y)-cos(x + y) = 1/2 then the values of x & y lying between...

    Text Solution

    |

  19. If tan x + tan 2x + tan 3x = 0 then which of the following can hold go...

    Text Solution

    |

  20. Along a road lies an odd number of stones placed at intervals of 10m. ...

    Text Solution

    |