The zeros of ax² + 3x + 7 = 0 are reciprocals of the roots to x² + bx + 2 = 0. Find a and b.
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

The trick here is to realise the significance of the constants in each equation and the significance of the central term. If we call the zeroes of equation 1 X1 and X2 then the zeroes of equation 2 are 1/X1 and 1/X2. (The factors of a quadratic can be written as (x-X1)(x-X2)=x^2-(X1+X2)x+X1X2.) The product of the zeroes are the respective constants so first divide equation 1 through by a: x^2+3x/a+7/a. X1X2=7/a and 1/X1X2=2, so X1X2=1/2=7/a. Therefore a=14. Also, X1+X2=-3/a and 1/X1+1/X2=-b=(X1+X2)/X1X2=-6/a=-6/14=-3/7, because we know X1+X2=-3/a and X1X2=1/2. Therefore, b=3/7 and the expressions are 14x^2+3x+7 and x^2+3x/7+2. The two equations become 14x^2+3x+7=0 and 7x^2+3x+14=0. Both have complex zeroes.

by Top Rated User (1.2m points)

Related questions

1 answer
1 answer
1 answer
asked Feb 18, 2013 in Algebra 2 Answers by anonymous | 1.0k views
1 answer
asked Oct 7, 2011 in Algebra 2 Answers by anonymous | 955 views
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
731,356 users