Determine a third-degree polynomial with integer coefficients and roots 1/2, 1/3 and 1/4.

Well, I know that we can write the polynomial as

\(\displaystyle (x-1/2)(x-1/3)(x-1/4)=0\)

\(\displaystyle x^3 - \frac{13 x^2}{12} + \frac{3 x}{8} - \frac{1}{24} = 0\)

\(\displaystyle \frac{1}{24}(24 x^3 - 26 x^2 + 9 x - 1) = 0\)

\(\displaystyle 24 x^3 - 26 x^2 + 9 x - 1 = 0\)

Is this the form they are after?

Also, does anyone have any good math books recommendations?

Well, I know that we can write the polynomial as

\(\displaystyle (x-1/2)(x-1/3)(x-1/4)=0\)

\(\displaystyle x^3 - \frac{13 x^2}{12} + \frac{3 x}{8} - \frac{1}{24} = 0\)

\(\displaystyle \frac{1}{24}(24 x^3 - 26 x^2 + 9 x - 1) = 0\)

\(\displaystyle 24 x^3 - 26 x^2 + 9 x - 1 = 0\)

Is this the form they are after?

Also, does anyone have any good math books recommendations?

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