SOLUTION: Without solving, determine the character of the solutions of each equation in the complex number system. 4x^2 + 12x + 9 =0

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Question 736470: Without solving, determine the character of the solutions of each equation in the complex number system.
4x^2 + 12x + 9 =0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In the quadratic formula for finding roots,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+, the
discriminant is ++b%5E2-4%2Aa%2Ac+
This determines the types of solutions
+4x%5E2+%2B+12x+%2B+9+=0+
+a+=+4+
+b+=+12+
+c+=+9+
+b%5E2+-+4%2Aa%2Ac+=+12%5E2+-+4%2A4%2A9+
+b%5E2+-+4%2Aa%2Ac+=+144+-+144+
----------------
The discriminant is +0+, so there is a single solution,
called a double root +x+=+-b%2F%282a%29+
Here's the plot:
+graph%28+400%2C+400%2C+-4%2C+2%2C+-2%2C+10%2C+4x%5E2+%2B+12x+%2B+9+%29+