Question 84902: Please help I need to know do these Quadriac Equations have a solution or not. And how to justify the answer.
a) 5x^2 + 8x + 7 = 0
b) (7)^1/2y^2 - 6y - 13(7)^1/2 = 0
c) 2x^2 + x - 1 = 0
d) 4/3x^2 - 2x + 3/4 = 0
e) 2x^2 + 5x + 5 = 0
f) p^2 - 4p + 4 = 0
g) m^2 + m + 1 = 0
h) 3z^2 + z - 1 = 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I need to know do these Quadriac Equations have a solution or not. And how to justify the answer.
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Check out b^2-4ac for each problem.
If it is >0 you have two Real number solutions
If it is =0 you have two equal Real number solutions
If it is <0 you have no Real number solutions; the solutions are complex.
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a) 5x^2 + 8x + 7 = 0
Example: 8^2-4*5*7<0, so no Real number solutions
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b) (7)^1/2y^2 - 6y - 13(7)^1/2 = 0
c) 2x^2 + x - 1 = 0
Example: 1^2-4*2*-1>0, so two Real number solutions
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d) 4/3x^2 - 2x + 3/4 = 0
Multiply thru by 12 to get:
16x^2 - 24x + 9 = 0
Example: 24^2-4*16*9 = 0, so two equal Real number solutions
e) 2x^2 + 5x + 5 = 0
f) p^2 - 4p + 4 = 0
g) m^2 + m + 1 = 0
h) 3z^2 + z - 1 = 0
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Cheers,
Stan H.
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