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15 October, 11:25

If α and β are the zeroes of 4x2 + 12x + 9, form a quadratic polynomial whose zeroes are α-1 and β-1

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  1. 15 October, 12:20
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    Given the quadratic equation:

    4x^2+12x+9

    the zeros are found by factorizing:

    4x^2+12x+9

    4x^2+6x+6x+9

    2x (2x+3) + 3 (2x+3)

    = (2x+3) (2x+3)

    hence the zeros are:

    x=-3/2 and x=-3/2

    thus

    α=-3/2 and β=-3/2

    thus

    α-1=-3/2-1=-5/2

    β-1=-3/2-1=-5/2

    thus the polynomial formed by above will be having roots:

    x=-5/2

    x+5/2==0

    hence

    2x+5=0

    thus the roots are:

    (2x+5) and (2x+5)

    the polynomials are:

    (2x+5) (2x+5)

    =4x^2+20x+25
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