You can put this solution on YOUR website! List all possible rational roots of 24x^3+2x-7 using Rational Roots Theorem.
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f(0) = -7 and f(1) = 19 so there must be a root between x=0 and x = 1.
I used a TI-84 to find a root at x = 0.62134943...
Cheers,
Stan H.