Home
Class 12
MATHS
Let alpha, beta in R. If alpha, beta^(2)...

Let `alpha, beta in` R. If `alpha, beta^(2)` are the roots of quadratic equation `x^(2) - px + 1 = 0` and `alpha^(2), beta` are the roots of quadratic equation `x^(2) -px + 8 = 0` , then find p, q , `alpha, beta`.

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta in R If alpha,beta^(2) are the roots of quadratic equation x^(2)-px+1=0. and alpha^(2),beta are the roots of quadratic equation x^(2)-qx+8=0, then find p,q,alpha,beta.

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

If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha^2 + beta^2

If alpha,beta, are the roots of quadratic equation 7x^(2)-13x-2=0 then find (alpha+beta)/(alpha beta)

If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha/beta + beta/alpha

If alpha and beta are the roots of the quadratic equation 2x^2+6x-5=0 , then find (alpha+beta) and alpha xx beta .

If alpha and beta are the roots of the quadratic equation 2x^2+6x-5=0 , then find (alpha+beta) and alpha xx beta .

If alpha,beta are the roots of the equation x^(2)+px+q=0, then -(1)/(alpha),-(1)/(beta) are the roots of the equation.

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

CENGAGE-THEORY OF EQUATIONS-Examples
  1. Find a quadratic equation whose product of roots x1a n dx2 is equal...

    Text Solution

    |

  2. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

    Text Solution

    |

  3. Let alpha, beta in R. If alpha, beta^(2) are the roots of quadratic eq...

    Text Solution

    |

  4. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

    Text Solution

    |

  5. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  6. Let n in Z and DeltaABC be a right tirangle with angle at C . If sin ...

    Text Solution

    |

  7. Find the value of a for which one root of the quadratic equation (a^2-...

    Text Solution

    |

  8. Find t values of the parameter a such that the rots alpha,beta of the ...

    Text Solution

    |

  9. Let a, b, c be real numbers with a = 0 and let alpha,beta be the root...

    Text Solution

    |

  10. Let alpha and beta be the roots of x^2 - 5x - 1 = 0 then the value of ...

    Text Solution

    |

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

    Text Solution

    |

  12. If alpha and beta are roots of the equatioin a cos theta + b sin theta...

    Text Solution

    |

  13. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

    Text Solution

    |

  14. If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c ...

    Text Solution

    |

  15. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that p...

    Text Solution

    |

  16. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

    Text Solution

    |

  17. The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c...

    Text Solution

    |

  18. If a ,b ,p ,q are nonzero real numbers, then how many oon roots would ...

    Text Solution

    |

  19. a ,b ,c are positive real numbers forming a G.P. ILf a x 62+2b x+c=0a ...

    Text Solution

    |

  20. Find the condition on a , b ,c ,d such that equations 2a x^2+b^2+c x+d...

    Text Solution

    |