use the rational zeros theorem to write a list of all potential rational zeros. then determine which ones are zeros
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Since 1 is the constant and the only roots of 1 have a magnitude of 1, we can see that ax=1 or ax=-1 is a root, where a is a constant. If we put x=1 into the function, it does in fact equal zero. So x-1 is a factor, which we can divide by, using synthetic division: 6x^2+6x+1. Therefore f(x)=(x-1)(6x^2+6x+1). The quadratic implies that we have to look at the factors of 6 (that is 6 and 1, and 2 and 3) and the factors of 1 (that is 1 and 1, and -1 and -1) and combine these possibilities to get the coefficient of the middle term, which is 6. We also know that from the sign of the constant we have to add the products of the prospective factors, and we know from that that we can have no minus signs. So we're looking for 1 and 1 as the constants, and the products are 2*1+3*1=5 or 6*1+1*1=7. Neither of these gives us the 5 we need. The solution of the quadratic is x=(-6+sqrt(36-24))/12=(-3+sqrt(3))/6=-0.2113 or -0.7887. Therefore the three roots are 1, -0.2113, -0.7887 approx.

by Top Rated User (1.2m points)

Related questions

1 answer
1 answer
1 answer
2 answers
asked May 3, 2011 in Algebra 1 Answers by anonymous | 2.3k views
1 answer
1 answer
asked Feb 20, 2013 in Algebra 2 Answers by anonymous | 559 views
0 answers
asked Nov 1, 2012 in Calculus Answers by anonymous | 766 views
0 answers
asked Nov 1, 2012 in Calculus Answers by anonymous | 558 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,279 answers
2,420 comments
732,309 users