1) Find the roots of the quadratic equation: 3x² – 2V6x + 2 = 0​

Question

1) Find the roots of the quadratic equation:
3x² – 2V6x + 2 = 0​

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Julia 1 month 2021-08-13T08:07:21+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-13T08:08:47+00:00

    Answer:

    Step-by-step explanation:

    3x²-2√6x+2=0

    3x²-√6x-√6x+2=0

    √3x(√3x-√2)-√2(√3x-√2)=0

    (√3x-√2)(√3x+√2)=0

    x=-√3/√2, √2/√3

    0
    2021-08-13T08:08:53+00:00

    Step-by-step explanation:

    3x² – 2√6x + 2 = 0

    3 {x}^{2}  -  \sqrt{6} x -  \sqrt{6}x + 2

     \sqrt{3} x( \sqrt{3} x -  \sqrt{2} ) -  \sqrt{2} ( \sqrt{3} x -  \sqrt{2} )

     ( \sqrt{3} x -  \sqrt{2} )( \sqrt{3} x -  \sqrt{2} )

    So, the roots of the equation are the values of x for which

    ( \sqrt{3} x -  \sqrt{2} )( \sqrt{3} x -  \sqrt{2} )

    Now,

    \sqrt{3} x -  \sqrt{2}  = 0

    x =   \sqrt{ \frac{2}{3} }

    So, this root is repeated twice, one for each repeated factor √3x-√2

    therefore the roots of 3x² – 2√6x + 2 = 0 are

     \sqrt{ \frac{2}{3} }  \: and \:  \sqrt{ \frac{2}{3} }

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