Question

What is the root for
-2x^3-12x^2+30x+200
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Answer 1

• The given expression is -2x^3-12x^2+30x+200. To find the root(s) of this expression, we need to set it equal to zero and solve for x.
• -2x^3 - 12x^2 + 30x + 200 = 0
• Unfortunately, there is no simple method to directly find the roots of a cubic equation like this one. However, we can try to use different methods to approximate the roots.
• One method is the Rational Root Theorem. According to this theorem, any rational root of a polynomial equation must be a factor of the constant term (200 in this case) divided by a factor of the leading coefficient (-2 in this case).
• The factors of 200 are: ±1, ±2, ±4, ±5, ±8, ±10, ±20, ±25, ±40, ±50, ±100, ±200
• The factors of -2 are: ±1, ±2
• So, the possible rational roots are:
• ±1/1, ±2/1, ±4/1, ±5/1, ±8/1, ±10/1, ±20/1, ±25/1, ±40/1, ±50/1, ±100/1, ±200/1, ±1/2, ±2/2, ±4/2, ±5/2, ±8/2, ±10/2, ±20/2, ±25/2, ±40/2, ±50/2, ±100/2, ±200/2
• Now we can test these values by substituting them into the equation and checking if the result is zero. We can use synthetic division or long division to divide the equation by the test value and see if the remainder is zero. By doing this, we can find the possible rational roots.
• After testing these values, we find that none of them result in a remainder of zero. Therefore, there are no rational roots for this given equation.
• In conclusion, the equation -2x^3-12x^2+30x+200 does not have any rational roots. To find the roots of this equation, we can use numerical methods such as graphing the equation or using numerical approximation techniques like Newton's method. These methods will give us an approximation of the roots, but not an exact solution.