If the roots \alpha\ \text{and}\ \beta of the equation, x^2-\sqrt2x+c=0

bacasauvfl

bacasauvfl

Answered question

2022-04-23

If the roots α and β of the equation, x22x+c=0 are complex for some real numbers c1 and |αβ1αβ|=1 then a value of c is

Answer & Explanation

vanvanvan4ie

vanvanvan4ie

Beginner2022-04-24Added 12 answers

With the help of the comments above, I am able to solve the question. Here is my solution:
Since the roots are complex, so when we square the given expression, we need to use |z|2=zz. Thus,
αβ1αβαβ1αβ=1
And since, complex roots are conjugate of each other. So, by replacing α with β and β with α, we get
(αβ1αβ)2=1
Thus, quadratic in c becomes
c26c+3=0
Thus, c=3±6

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?