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Answer :
Final answer:
To solve the equation 15x^4 + 25x^3 + 10x^2, factor out the greatest common factor and set each factor equal to zero. Solve the resulting quadratic equation to find the solutions.
Explanation:
To solve the equation 15x^4 + 25x^3 + 10x^2, we can factor out the greatest common factor, which in this case is 5x^2. This gives us 5x^2(3x^2 + 5x + 2). Now we can solve for x by setting each factor equal to zero and solving the resulting quadratic equation.
The equation 3x^2 + 5x + 2 = 0 can be factored as (x + 1)(3x + 2) = 0. Setting each factor equal to zero gives us x + 1 = 0 and 3x + 2 = 0. Solving these equations gives us x = -1 and x = -2/3.
Therefore, the solutions to the equation 15x^4 + 25x^3 + 10x^2 = 0 are x = -1 and x = -2/3.
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