SOLUTION: Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots.

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Question 1054587: Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The roots can be imaginary.
Suppose the equation is:
+y+=+x%5E2+-+2x+%2B+2+
Find the roots:
+x%5E2+-+2x+%2B+2+=+0+
Complete the square:
+x%5E2+-+2x+=+-2+
+x%5E2+-+2x+%2B+%28-2%2F2%29%5E2+=+-2+%2B+%28-2%2F2%29%5E2+
+x%5E2+-+2x+%2B+1+=+-2+%2B+1+
+%28+x+-+1+%29%5E2+=+-1+
Take the square root of both sides
+x+-+1+=+squart%28-1%29+
+x+-+1+=+i+
+x+=+1+%2B+i+
and, taking the negative +sqrt%28-1%29+,
+x+-+1+=+-i+
+x+=+1+-+i+
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The roots are +1+%2B+i+ and +1+-+i+
----------------
Here's the plot:
+graph%28+400%2C+400%2C+-7%2C+7%2C+-7%2C+7%2C+x%5E2+-+2x+%2B+2+%29+
Note there are no x-crossings