SOLUTION: 10zē+3z-3=0 I need to know what is the discriminant? Is it positive or negative? What kind of solution would you get if the discriminant were negative? Thank You!

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Question 744036: 10zē+3z-3=0 I need to know what is the discriminant? Is it positive or negative? What kind of solution would you get if the discriminant were negative?
Thank You!

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
10zē+3z-3=0 I need to know what is the discriminant?
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Disc = b^2 - 4ac
a = 10
b = 3
c = -3
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Disc = 10^2 - 4*10*-3
= 100 + 120
= 220
There's no mystery about it.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation has the form
+ax%5E2+%2B+b%2Ax+%2B+c+ , then the roots are found
using the quadratic formula:
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
The discriminant is:
+b%5E2+-+4a%2Ac+
If the discriminant is positive, both roots are real
If the discriminant is negative, both roots are imaginary
If the discriminant is zero, there is 1 real root
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Your equation is:
+10z%5E2+%2B+3z+-+3+=+0+
+a+=+10+
+b+=+3+
+c+=+-3+
and the discriminant is:
+b%5E2+-+4%2Aa%2Ac+=+3%5E2+-+4%2A10%2A%28-3%29+
+b%5E2+-+4%2Aa%2Ac+=+9+%2B+120+
+b%5E2+-+4%2Aa%2Ac+=+129+
This result is positive, so there are 2 real roots
Here is the plot:
+graph%28+400%2C+400%2C+-3%2C+3%2C+-5%2C+5%2C+10x%5E2+%2B+3x+-+3+%29+