\(\displaystyle{x}^{{{2}}}+{2}{a}{x}+{b}={0}\) where \(\displaystyle{x}_{{{1}}}\) and \(\displaystyle{x}_{{{2}}}\)

zatajuxoqj

zatajuxoqj

Answered question

2022-04-01

x2+2ax+b=0 where x1 and x2 are real solutions.
For which value of b function f(b)=|x1x2| reaches maximum if |x1x2|=2m

Answer & Explanation

Tristatex9tw

Tristatex9tw

Beginner2022-04-02Added 18 answers

Step 1
We need a2b>0, that is a2>b
a2bm2
ba2m2
In summary,
b[a2m2,a2)
Jaslyn Allison

Jaslyn Allison

Beginner2022-04-03Added 13 answers

Step 1
The discriminant must be positive, i.e.
a2b>0
The maximum difference of the roots is 2m, and the minimum difference is zero when a2b0. So
0<2a2b2m
0<a2bm2
m2ba2<0
a2m2b<a2
Hence,
b[a2m2,a2)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?