We've learned that the roots of the quadratic equation ах+bx+с-0 are given by the quadratic formula --b±vB²-4ac 2 a When roundoff error is considered we find that there is a more numerically accurate version of this formula. Leť's assume b>0 (if it isn't we can multiply the entire equation by –1 ). (a) Show that if |b+Vb²–4ac b+\b²- then are identical to the roots given by the quadratic formula. (b) Using a calculator or the Scilab console, calculate the roots of x²+10*x+1=0 using both the quadratic formula and the alternate formula given in (a). Do you get the same answers? (c) Show that the quadratic formula can be rewritten as 4 ас b 171- 2a r=-

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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We've learned that the roots of the quadratic equation
ax²+bx+c=0
are given by the quadratic formula
-b+\b-4 ac
r =
2 a
When roundoff error is considered we find that there is a more numerically accurate version of
this formula. Let's assume b>0 (if it isn't we can multiply the entire equation by –1 ).
(a) Show that if
q=-
|b+v
then
a
are identical to the roots given by the quadratic formula.
(b) Using a calculator or the Scilab console, calculate the roots of
x²+10*x+1=0
using both the quadratic formula and the alternate formula given in (a). Do you get the same
answers?
(c) Show that the quadratic formula can be rewritten as
b
r=-
2a
4 ac
b²
Transcribed Image Text:We've learned that the roots of the quadratic equation ax²+bx+c=0 are given by the quadratic formula -b+\b-4 ac r = 2 a When roundoff error is considered we find that there is a more numerically accurate version of this formula. Let's assume b>0 (if it isn't we can multiply the entire equation by –1 ). (a) Show that if q=- |b+v then a are identical to the roots given by the quadratic formula. (b) Using a calculator or the Scilab console, calculate the roots of x²+10*x+1=0 using both the quadratic formula and the alternate formula given in (a). Do you get the same answers? (c) Show that the quadratic formula can be rewritten as b r=- 2a 4 ac b²
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