Find all the values of a for which

Harold Hoover

Harold Hoover

Answered question

2022-04-04

Find all the values of a for which both the root of the equation (a2)x22ax+a=0 lies in the interval (2,1),

Answer & Explanation

davane6a7a

davane6a7a

Beginner2022-04-05Added 8 answers

Step 1
(a2)x22ax+a=0
The roots are:
r1,r2=aa28a2(a2)
Step 2
As you've found, to satisfy the quadratic equation, and 2<r1,r2<1, we require 0a<89.
It may be a matter of semantics, but there is no such thing as "both roots" if there is only one root!
If a=0, there is a double root: r1=r2=0.

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