Use the rational root theorem to determine which of the following could not be a root of 6x^3+23x^2-6x-8=0
I need all of the steps.
Thanks
I don't see any "following"
If any given, simply sub in the value to see which one works.
Sure! Here are the steps to determine which of the following options could not be a root of the equation 6x^3 + 23x^2 - 6x - 8 = 0 using the Rational Root Theorem:
Step 1: Write down the equation: 6x^3 + 23x^2 - 6x - 8 = 0.
Step 2: Identify the coefficients of the terms in the equation. In this case, the coefficients are 6, 23, -6, and -8.
Step 3: Apply the Rational Root Theorem. According to the theorem, any rational root of the equation must be of the form ±(factor of constant term) / (factor of leading coefficient).
Step 4: Determine the factors of the constant term (-8): ±1, ±2, ±4, ±8.
Step 5: Determine the factors of the leading coefficient (6): ±1, ±2, ±3, ±6.
Step 6: Generate a list of possible rational roots by combining the factors. This means taking a factor of the constant term and dividing it by a factor of the leading coefficient. In this case, the possible rational roots are:
±1/1, ±1/2, ±1/3, ±1/6, ±2/1, ±2/2, ±2/3, ±2/6, ±4/1, ±4/2, ±4/3, ±4/6, ±8/1, ±8/2, ±8/3, ±8/6.
Step 7: Simplify the list of rational roots. For example, ±2/2 simplifies to ±1, ±2/6 simplifies to ±1/3, ±8/2 simplifies to ±4, and ±8/6 simplifies to ±4/3.
Step 8: Test each simplified rational root by substituting it into the original equation 6x^3 + 23x^2 - 6x - 8 = 0 to check if the equation equals zero. If it does, then that root is a valid solution. If it does not, then that root is not a solution.
By going through this process, you can determine which of the given options could not be a root of the equation.