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Two roots of quadratic equations are giv...

Two roots of quadratic equations are givne, frame the equation :
`1-3sqrt5and1+3sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)-2x-44=0` is the required quadratic equation.
Let `alpha=1-3sqrt5andbeta=1+3sqrt5`
Then `alpha+beta=1-3sqrt5+1+3sqrt5=2`
`alphabeta=(1-3sqrt5)(1+3sqrt5)`
`=(1)^(2)-(3sqrt5)^(2)=1-45=-44`
The required quadratic equation is
`x^(2)-(alpha+beta)x+alphabeta=0`
i.e. `x^(2)-(2)x+(-44)=0`
i.e. `x^(2)-2x-44=0`
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Knowledge Check

  • The roots of a quadratic equation are 5 and -2 . Then, the equation is

    A
    `x^(2)-3x+10=0`
    B
    `x^(2)-3x-10=0`
    C
    `x^(2)+3x-10=0`
    D
    `x^(2)+3x+10=0`

  • If the roots of a quadratic equation are -1 and 3, then the quadratic equation is

    A
    `x^2-2x-3=0`
    B
    `x^2+2x-3=0`
    C
    `x^2-2x+3=0`
    D
    `x^2+2x+3=0`

  • If the roots of the quadratic equation are (-1)/(2) and 3/2 , then the equation is

    A
    `4x^(2) -6x+3=0`
    B
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    C
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    D
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    • NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUADRATIC EQUATION -PROBLEM SET -18
    1. Two roots of quadratic equations are givne, frame the equation : 1-...

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    2. Two roots of quadratic equations are given, frame the equation. 0 an...

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    3. Determine the nature of roots for each of the quadratic equations. 3...

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    4. Determine the nature of the roots for each of the following quadratic...

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    5. Determine the nature of roots for each of the quadratic equations. m...

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    6. Solve the following quadratic equations : 1/(x+5)=1/x^(2)

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    7. Solve the following quadratic equations: x^(2)-(3x)/(10)-1/(10)=0

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    8. Solve the following quadratic equations: (2x+3)^(2)=25

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    9. Solve the following quadratic equations : m^(2)+5m+5=0

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    10. Solve the following quadratic equations : 5m^(2)+2m+1=0

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    11. Solve the following quadratic equations : x^(3)-4x-3=0

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    12. Find m, if the quadratic equation (m-12)x^(2)+2(m-12)x+2=0 has real an...

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    13. The sum of two roots of a quadratic equation is 5 and the sum of their...

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    14. Find quadratic equation such that its roots are square of sum of the r...

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    15. Mukund possesses RS 50 more than what Sagar possesses. The product of ...

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    16. The difference between the squares of two numbers is 120. The square o...

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    17. Mr. Dinesh owns an agricultural farm at village Talvel. The length of ...

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