find all the zeroes of the polynomial 2x^4+5x^3-11x^2-20x+12 if two of its zeroes are 2 and -2
in Other Math Topics 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

Since two zeroes are 2 and -2, (x-2)(x+2)=x^2-4 must be a factor. Algebraic long division gives us:

            2x^2+5x-3 = (2x-1)(x+3) so the other zeroes are 1/2 and -3.

x^2-4 ) 2x^4+5x^3-11x^2-20x+12

            2x^4           -8x^2

                     5x^3  -3x^2-20x

                     5x^3           -20x

                               -3x^2       +12

                               -3x^2       +12

                                        0

 

                              

by Top Rated User (1.0m points)
We know if x=a is a zero of a polynomial and then x-a is a factor of f(x). Since 2 and -2 are zeros of f(x) Therefore: (x-2) (x+2) = x²-4 (x²-4) is a factor of f(x) Now, we divide 2x⁴-5x³-11x²+20x+12 by g(x)=(x²-4) to find the zero f(x). By using division algorithm we have, f(x)=g(x)×q(x)-r(x) 2x⁴-5x³-11x²+20x+12=(x²-4)(2x²-5x-3) = (x-2)(x+2)[2x(x-3)+1(x-3)] =(x-2)(x+2)(x-3)(2x+1) Hence the zeros of the polynomial are; 2,-2,3,-1/2
by
5 Common Cat Behaviours And What Th...
5 Common Cat Behaviours And What They Mean

Related questions

2 answers
asked May 26, 2013 in Pre-Algebra Answers by anonymous | 2.1k views
1 answer
asked Jun 19, 2014 in Other Math Topics by anonymous | 380 views
1 answer
asked May 28, 2013 in Algebra 2 Answers by anonymous | 341 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!
87,138 questions
97,020 answers
2,373 comments
24,439 users