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8 May, 01:12

X^3/2 - 2x^3/4 + 1 = 0

solve the equation (hint: it is quadratic in form)

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  1. 8 May, 01:31
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    The correct factorization of this polynomial is (x^3/4 - 1) (x^3/4 - 1)

    The reason this can be factored is that the middle term has half of the exponent as the lead term. So we can just substitute them to a more standard from and then substitute back at the end. So, for ease sake, we'll make the lead exponent 2 and the middle exponent 1.

    x^2 - 2x + 1

    Now to factor this, we look for factors of 1 that multiply to - 2. This is clearly - 1 and - 1. So we use them in a parenthesis with the x term.

    (x - 1) (x - 1)

    Now, since we put x in for x^3/4 at the beginning, we make that switch back now.

    (x^3/4 - 1) (x^3/4 - 1)
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