Home
Class 10
MATHS
If sqrt2and-1 be two roots of the quadra...

If `sqrt2and-1` be two roots of the quadratic equation `sqrt2ax^(2)+bx+1=0`, then find the values of a and b.

Text Solution

Verified by Experts

The correct Answer is:
`a=(1)/(2),b=-(2+sqrt2)/(2);`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.3|43 Videos

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.4|28 Videos

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.1|29 Videos

  • PYTHAGORAS THEOREM

    CALCUTTA BOOK HOUSE|Exercise EXAMPLE 6|4 Videos

  • QUADRATIC SURDS

    CALCUTTA BOOK HOUSE|Exercise Exercise -3.2|28 Videos

Similar Questions

Explore conceptually related problems

If (2)/(5)and-5 be two roots of the quadratic equation ax^(2)-5x+b=0 , then find the values of a and b.

If -5 and -7 be two roots of the equation ax^(2)+bx+35=0 , then find the values of a and b.

If one root of the quadratic equation be (3+sqrt2) , then find the equation.

If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0 , then find the values of alpha+beta+1

If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0 , then find the value of the following quantities : (1)/(aalpha+b)+(1)/(abeta+b)

If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0 , then find the value of the following quantities : (aalpha+b)^(-2)+(abeta+b)^(-2)

If alphaandbeta be the roots of the quadratic equation ax^(2)+bx+c=0 , then find the quadratic equation whose roots are ((1)/(alpha)+1)and((1)/(beta)+1) .

Two roots of the equation ax^2 +bx +c=0 is alpha,beta then find the value of alpha^2 + beta^2

Two roots of the equation ax^2 +bx +c=0 is alpha,beta then find the value of alpha^3 + beta^3

Short-answer type questions (S.A.) : If one root of the quadratic equation 3x^(2)+sqrt2x+a=0" be "sqrt2 , then find the value of a.

CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.2
  1. The quadratic equation in one variable x^(2)+1=0 have no roots.

    Text Solution

    |

  2. The roots of the quadratic equation x^(2)+a=0 are .

    Text Solution

    |

  3. The roots of the quadratic equation x^(2)-2x+1=0 are and .

    Text Solution

    |

  4. Solve : sqrtx+(1)/(sqrtx)=2.

    Text Solution

    |

  5. Determine for value of a if sqrt2 is a root of the quadratic equation ...

    Text Solution

    |

  6. Prove that p and q are two roots of the quadratic x^(2)-(p+q)x+pq=0.

    Text Solution

    |

  7. Solve : x+(k)/(x)=sqrt2.

    Text Solution

    |

  8. If (2)/(5)and-5 be two roots of the quadratic equation ax^(2)-5x+b=0, ...

    Text Solution

    |

  9. If sqrt2and-1 be two roots of the quadratic equation sqrt2ax^(2)+bx+1=...

    Text Solution

    |

  10. Solve the equations : x^(2)+2bx-b^(2)=a^(2)-b(b-2x)

    Text Solution

    |

  11. Solve the equations : (b-ax)/(bx-a)=(d-cx)/(dx-c)

    Text Solution

    |

  12. Solve the equations : (1)/(a-b){a^(2)(x-b)-b^(2)(x-a)}=x^(2)

    Text Solution

    |

  13. Solve the equations : (x-3)/(x+3)-(x+3)/(x-3)+6(6)/(7)=0

    Text Solution

    |

  14. Solve the equation abs(x-abs(4-x))-2x=4

    Text Solution

    |

  15. Solve the equations : (x-3)/(x+3)+(x+3)/(x-3)=(2(x+4))/(x-4)

    Text Solution

    |

  16. Solve the equations : ((a-x)/(x+a))^(2)-5((x-a)/(x+a))+6=0

    Text Solution

    |

  17. Solve the equations : ((x+1)^(3)-(x-1)^(3))/((x+1)^(2)-(x-1)^(2))=2

    Text Solution

    |

  18. Solve the equations : (x-a)/(x-b)+(x-b)/(x-a)=(a)/(b)+(b)/(a)

    Text Solution

    |

  19. Solve the equations : (1)/(a+b-x)=(1)/(a)+(1)/(b)-(1)/(x)

    Text Solution

    |

  20. Solve the equations : (x-2)(x-3)-(a+1)/(a^(2))=0

    Text Solution

    |