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27x^(2) - 10x +1=0...

`27x^(2) - 10x +1=0`

Text Solution

Verified by Experts

The correct Answer is:
`5/27 +- sqrt(2)/27`I
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Knowledge Check

  • The roots of x^(4) - 10x^(3) + 26x^(2) - 10x + 1 = 0 are

    A
    `3 pm 2 sqrt(2), 2 pm sqrt(3) `
    B
    `2 pm 3 sqrt(2), 2 pm sqrt(3) `
    C
    `3 pm 2 sqrt(2), 3 pm sqrt(2)`
    D
    `2 pm 3 sqrt(2) , 3 pm sqrt(2)`

  • Match the following i. The equation whose roots are multiplied by 3 of " " (a) x^(3) - 8x^(2) + 19x - 15 = 0 those of x^(3) + 2x^(2) - 4x + 1 =0 is ii.The equation whose roots are exceed by 1 than " " (b) x^(3) + 5x^(2) + 10x + 10 = 0 those of x^(3) - 5x^(2) + 6x - 3 = 0 is iii. The equation whose roots are diminish by 1 than " " (c ) 4x^(4) - 2x^(3) + 6x^(2) - 3x - 1 =0 those of x^(3) + 2x^(2) + 3x + 4 =0 is iv. The equation whose roots are the reciprocals of the " " (d) x^(3) + 6x^(2) - 36x + 27 = 0 roots of x^(4) + 3x^(3) - 6x^(2) + 2x - 4 = 0 is

    A
    c, d, a, b
    B
    d, c, b, a,
    C
    c, a , b, d
    D
    c, b, a, d

  • The cubic equation whose roots are the squares of the roots of x^(3) - 2x^(2) + 10x - 8 = 0 is

    A
    `x^(3) + 8x^(2) + 68x - 64 = 0`
    B
    `x^(3) + 16x^(2) - 68x - 64 = 0`
    C
    `x^(3) - 16x^(2) + 68x - 64 =0`
    D
    `x^(3) + 16x^(2) + 68x - 64 = 0`

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    Assertion (A): The roots of the equation 2x^(2) - 15x + 4 = 0 are each increased by 3, then the new equation is 2x^(2)-27x + 67 = 0 Reason (R): The equation whose roots are increased by k then those of f(x) = 0 is f(x//k) = 0

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