SOLUTION: Solve the problem. Solve the equation 12x to third power - 77x to second power + 91x - 30 = 0 given that 2/3 is a root.
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Question 137337: Solve the problem. Solve the equation 12x to third power - 77x to second power + 91x - 30 = 0 given that 2/3 is a root. Found 2 solutions by solver91311, Edwin McCravy:Answer by solver91311(24713) (Show Source):
If is a root of the equation, then is a factor of the cubic polynomial.
Use polynomial long division to divide by . Since is a factor and you are dividing a 1st degree polynomial into a 3rd degree polynomial, the quotient will be a quadratic with no remainder. Solve the quadratic by normal methods to obtain the two missing roots to the original equation.
You can put this solution on YOUR website! Solve the problem. Solve the equation 12x to third power - 77x to second power + 91x - 30 = 0 given that 2/3 is a root.
given that is a root.
Since is a root, then the polynomial is divisible by
So we can divide that synthetically this way:
| 12 -77 91 -30
| 8 -46 30
---------------
12 -69 45 0
So we have factored the polynomial this way
Now we can factor a 3 out of the second parentheses, getting:
Factor the trinomial in the second parentheses
If you like you can move the factor in front of
the first factor:
and distribute the 3 into the
That's the complete factorization of the
original polynomial. Now we use the zero-factor
principle and set each factor equal to 0
gives solution which we knew from the start.
gives solution gives solution
Edwin
