SOLUTION: Describe the nature and the number of the solutions of 2x^2-7x+9=x+1

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Question 554524: Describe the nature and the number of the solutions of 2x^2-7x+9=x+1
Found 2 solutions by josmiceli, kkasko:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is determined by what is called the " discriminant "
This is +b%5E2+-+4a%2Ac+ in the formula for the roots
which is x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this case:
+2x%5E2-7x%2B9=x%2B1+
+2x%5E2+-7x+-+x%2B+9+-+1+=+0+
+2x%5E2+-+8x+%2B+8+=+0+
+x%5E2+-+4x+%2B+4+=+0+
+a+=+1+
+b+=+-4+
+c+=+4+
+b%5E2+-+4a%2Ac+=+%28-4%29%5E2+-+4%2A1%2A4+
+b%5E2+-+4a%2Ac+=+16+-+16+
The discriminant is zero, which means there is 1 solution,
which is called a double root. Here's a plot of the
equation. Notice it touches the x-axis at 1 point
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+-+4x+%2B+4+%29+

Answer by kkasko(46) About Me  (Show Source):
You can put this solution on YOUR website!
Describe the nature and the number of the solutions of 2x^2-7x+9=x+1
2x^2-7x+9=x+1
-x. -1
2x^2-8x+8=0
a=2 b=-8 c=8
b^2-4(a)(c)
-8^2-4(2)(8)
64-64
=0
The nature of the roots is two real equal roots. Meaning their really is only one solution. The solution is (2,0)