Solve the polynomial inequality x^{2}-2x+1>0 and graph the solution set on a

philosphy111of 2021-11-26 Answered
Solve the polynomial inequality
x22x+1>0
and graph the solution set on a real number line. Express the solution set in interval notation.
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Expert Answer

giskacu
Answered 2021-11-27 Author has 22 answers

Step 1
The given polynomial inequality is
x22x+1>0
To solve the inequality, find its critical points by equating it to zero.
x22x+1=0
x2xx+1=0
x(x1)1(x1)=0
(x1)(x1)=0
x=1, 1
Step 2
Now, make the sign analysis on Number line to determine about the inequality.
If x<1, then for the given polynomial the result is always positive and even if x>1, then also for the given polynomial the result is positive. Therefore, for all values of x except 1 ,the polynomial is positive.
image
Answer: Hence, the interval notation for the given polynomial inequality is
(, 1)(1, )

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