Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Determine the roots of 20x^2 - 22x + 6 = 0?

20x^2 - 22x + 6 = 0

8 Answers

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  • 2 months ago

    Substituting into the quadratic formula will be as follows:

    x =(-11+-sqrt(-11)^2 -4*10*6)/2*10)

    Doing the arithmetic, this turns out to be as follows:

    (-11+-sqrt (119)i)/20

  • ?
    Lv 7
    2 months ago

    The discriminant

    D=(-22)^2-4(20)(6)=4>0

    The equation has 2 distinct real roots.

    They are

    x=[22+/-2]/(40)

    =>

    x=3/5 or x=1/2.

  • ?
    Lv 7
    2 months ago

    Using the quadratic equation formula: x = 3/5 or x = 1/2

  • 2 months ago

    20x² - 22x + 6 = 0

    20x² - 22x = - 6

    x² - (22/20).x = - 6/20

    x² - (11/10).x = - 3/10

    x² - (11/10).x + (11/20)² = - (3/10) + (11/20)²

    x² - (11/10).x + (11/20)² = 1/400

    [x - (11/20)]² = 1/400

    x - (11/20) = ± 1/20

    x = (11/20) ± (1/20)

    x = (11 ± 1)/20

    x = (11 + 1)/20 = 12/20 = 3/5

    x = (11 ± 1)/20 = 10/20 = 1/2

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  • ?
    Lv 7
    2 months ago

    20x^2 - 22x + 6 = 0

    2 (2 x - 1) (5 x - 3) = 0

    x = 1/2

    x = 3/5

  • 2 months ago

    20x^2 - 22x + 6 = 0

    (4x - 2)(5x - 3) = 0

    4x - 2 = 0, 5x - 3 = 0

    x = 1/2 or x = 3/5 

    roots are 1/2 and 3/5..

  • 2 months ago

    2(5x-3)(2x-1)

    x=3/5

    x=1/2                       .

  • 2 months ago

    Divide both sides by 2:

    10x² - 11x + 3 = 0

    Multiply the outside coefficients --> 10 * 3 = 30

    You are looking for 2 numbers that multiply to be 30, but add to be the middle coefficient (-11). Obviously we need two negative numbers which are clearly -5 and -6.

    Split the middle term into -5x and -6x:

    10x² - 5x - 6x + 3 = 0

    Factor each pair:

    (10x² - 5x) - (6x - 3) = 0

    5x(2x - 1) - 3(2x - 1) = 0

    You have the repeated (2x - 1) so factor that out:

    (5x - 3)(2x - 1) = 0

    By the zero product rule, if ab=0 then a=0 or b=0:

    5x - 3 = 0

    5x = 3

    x = 3/5

    or

    2x - 1 = 0

    2x = 1

    x = 1/2

    Answer:

    x = 1/2 or x = 3/5

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