How to do a quick estimation if x_2 \ll x_1 holds for the roots of a quadratic equation - to a

gaitaprepeted05u

gaitaprepeted05u

Answered question

2022-04-22

How to do a quick estimation if x2llx1 holds for the roots of a quadratic equation - to apply quick and easy root-finding formula?
Vieta's formulas provide a useful method for finding the roots of a quadratic in the case where one root is much smaller than the other.
If |x2|ll|x1|, then x1+x2x1 and we have the estimate x1ba.

Answer & Explanation

haillarip0c9

haillarip0c9

Beginner2022-04-23Added 23 answers

One root is much smaller than the other when |ac|llb2 because then the square root in the quadratic formula is very close to b. The approximation given comes from replacing the square root by b and taking the minus sign so the two terms add. This is also the time that the calculation of the other root suffers from roundoff error in a computer because b+b24ac is the difference of two similar numbers.

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