Find all values of b for which the

Markelovnsl

Markelovnsl

Answered question

2022-04-15

Find all values of b for which the equations 1988x2+bx+8891=0 and 8891x2+bx+1988=0 have a common root.

Answer & Explanation

stecchiniror7

stecchiniror7

Beginner2022-04-16Added 14 answers

Observe that zero is not a root and if r0 is a root of the first, 1r will be a root of the second.
So, we should have r=1r
or r=±1.
Thus 1988±b+8891=0
chabinka61jx

chabinka61jx

Beginner2022-04-17Added 12 answers

Note that,
p(x)=1988x2+bx+8891q(x)=x2p(1x)=8891x2+bx+1981
Since p(0)0 we want b such that p(x), p(1x) have a common root.
It is easy to see that this implies that the common root, r, satisfies r=1r so that r±1.
And from there, the problem is straight forward.

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?