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Form polynomial equations of the lowest...

Form polynomial equations of the lowest degree , with roots as given below .
Hint : Equation having roots `alpha ,beta ,gamma` is `(x-alpha) (x-beta) (x-gamma) =0`
1,-1,3

Text Solution

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Required equation is
(x-1) (x+1) (x-3) =0
`rArr (x^2-1) (x-3)=0 `
`rArr x^3-3x^2-x +3=0 `
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Knowledge Check

  • If alpha , beta , gamma are the roots of x^(3) + 3x + 2 =0 then the equation whose roots alpha (beta + gamma), beta( gamma + alpha), gamma(alpha + beta) is

    A
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    D
    `x^(3) - 6x^(2) - 9x - 4 = 0`

  • If alpha, beta , gamma are the roots of 3x^(3) - 5x^(2) - 7x + 1 = 0 thent the equation whose roots are -alpha, -beta, - gamma is

    A
    `3x^(3) + 5x^(2) - 7x - 1 = 0 `
    B
    `9x^(3) + 6x^(2) - 4x - 1= `0
    C
    `x^(3) - 3x^(2) + 8x^(2) + 4 = 0`
    D
    `10x^(3) - 13x^(2) + 18x^(2) + 40` = 0

  • If alpha, beta , gamma are the roots of x^(3) + 3px + q = 0 then the equation whose roots are (alpha + 1)/( beta + gamma - alpha), (beta + 1)/(gamma + alpha - beta) and (gamma + 1)/(alpha + beta - gamma) is

    A
    `8y^(3) + 12y^(2) + (6 + 6p) y + 1 + 3p - q = 0 `
    B
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    C
    `8qy^(3) + 12 (q + p) y^(2) + 6(q - 2p)y + (q + 3p - 1) = 0 `
    D
    `8qy^(3) - 12(q - p) y^(2) - 6(q - 2p) y + (q - 3p + 1) = 0`

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