Find the roots for the equation:
\[ 24x^3 = 10x^2 + 4x \]
Verify your solutions by checking them in the original equation.
Answer (2)
24 x 3 = 10 x 2 + 4 x 24 x 3 − 10 x 2 − 4 x = 0 2 x ( 12 x 2 − 5 x − 2 ) = 0 2 x ( 12 x 2 + 3 x − 8 x − 2 ) = 0 2 x ( 3 x ( 4 x + 1 ) − 2 ( 4 x + 1 )) = 0 2 x ( 3 x − 2 ) ( 4 x + 1 ) = 0 x = 0 ∨ x = 3 2 ∨ x = − 4 1
The roots of the equation 24 x 3 = 10 x 2 + 4 x are x = 0 , x = 3 2 , and x = − 4 1 . All solutions were verified by substituting them back into the original equation, showing they hold true. Hence, the solutions are confirmed to be correct.
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