For what values of m will the equation x²-2mx+7m-12=0 has reciprocal roots?
in Algebra 1 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.

2 Answers

For what values of m will the equation x²-2mx+7m-12=0 has reciprocal roots?

Let there be reciprocal roots x1 = a and x2 = 1/a, where these two roots are reciprocal to each other.

Taking these roots as the solutions to a quadratic equation alows us to recreate the quadratic as,

(x - a)(x - 1/a) = 0

Multiplying out gives us,

x^2 - (a + 1/a)x + 1 = 0

Comparing this quadratic with the original x²-2mx+7m-12 = 0, and comparing the coefficient of x and the constant term,

-(a + 1/a) = -2m

1 = 7m - 12    ---> m = 13/7

The equation has reciprocal roots for m = 13/7

Then,

(a + 1/a) = 26/7

7a^2 + 7 = 26a

 7a^2 - 26a + 7 = 0

Solution here gives the reciprocal roots as a1 = 13/7 + (2/7)sqrt(30) and a2 = 13/7 - (2/7)sqrt(30)

by Level 11 User (81.5k points)
for all values of m answer is zero
by

Related questions

0 answers
3 answers
asked Feb 7, 2014 in Algebra 1 Answers by anonymous | 365 views
1 answer
asked Nov 2, 2015 in Other Math Topics by anonymous | 161 views
1 answer
asked Aug 18, 2014 in Algebra 2 Answers by Jennifer A. Cascaño Level 12 User (101k points) | 214 views
1 answer
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!
86,144 questions
92,138 answers
2,245 comments
23,900 users