SOLUTION: Good day to you all. Please determine the nature of the solutions to each equation without solving it. 1.) 25x^2 - 10x + 1 = 0 2.) x^2 + x +2 = 0 3.) 5x^2 - x = 0 Than

Algebra ->  Test  -> Lessons -> SOLUTION: Good day to you all. Please determine the nature of the solutions to each equation without solving it. 1.) 25x^2 - 10x + 1 = 0 2.) x^2 + x +2 = 0 3.) 5x^2 - x = 0 Than      Log On


   

Question 587200: Good day to you all.
Please determine the nature of the solutions to each equation without solving it.
1.) 25x^2 - 10x + 1 = 0
2.) x^2 + x +2 = 0
3.) 5x^2 - x = 0
Thank You.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Look at b%5E2+-+4%2Aa%2Ac+ where the
equation has the form +a%2Ax%5E2+%2B+b%2Ax+%2Bc+=+0+
(1)
+b%5E2+-+4%2Aa%2Ac+=+%28-10%29%5E2+-+4%2A25%2A1+
+b%5E2+-+4%2Aa%2Ac+=+100+-+100+
+b%5E2+-+4%2Aa%2Ac+=+0+
This means there is 1 real solution
It is called a double root
---------------------------------
(2)
+b%5E2+-+4%2Aa%2Ac+=+1%5E2+-+4%2A1%2A2+
+b%5E2+-+4%2Aa%2Ac+=+1+-+8+
+b%5E2+-+4%2Aa%2Ac+=+-7+
This is minus, so there are 2
imaginary roots ( look like a%2Bb%2Ai and a-b%2Ai )
-----------------------------------
(3)
+b%5E2+-+4%2Aa%2Ac+=+%28-1%29%5E2+-+4%2A5%2A0+
+b%5E2+-+4%2Aa%2Ac+=+1+
This is plus, so there are 2 real roots
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Here's plots of the 3 equations.
Touching the x-axis: 1 solution
Not touching at all: 2 imaginary solutions
Touching twice: 2 real solutions