math
posted by Alex .
Here's my question: Determine if each system has one, two, or no solutions. (Show your work  3 marks each)
a)y=2x^22x+1 and y=3x5
b)y=x^2+3x16 and y=x^28x18
Here's my work on the question:
a)
x=(b plus/minus sign (square root b^24ac)/(2a)
x=(2 plus/minus sign (square root 2^24(2)(1)/(2(2)
x=(2 plus/minus sign (square root 48)/(4)
x=( 2 plus/minus sign (nonreal answer)/(4)
x=(b plus/minus sign (square root b^24ac)/(2a)
x=(5 plus/minus sign (square root 5^24(3)/2(3)
x=(5 plus/minus sign(square root 2512)/6
x=(5 plus/minus sign(square root 37)/6
x=(5 plus/minus sign (nonreal answer)/6
b)
x=(b plus/minus sign (square root b^24ac)/(2a)
x=(3 plus/minus sign (square root 3^24(1)(16)/(2(1))
x=(3 plus/minus sign (square root 964)/2
x=(3 plus/minus sign (square root 73)/2
x=(3 plus/minus sign (8.54)/(2)
x=4.27
x=(b plus/minus sign (square root b^24ac)/(2a)
x=(8 plus/minus sign(square root 8^24(1)(18)/(2(1)
x=(8 plus/minus sign(square root6472)/(2)
x=(8 plus/minus sign(square root 136)/(2)
x=(8 plus/minus sign(nonreal answer)/(2)
Can you please help me where I went wrong and help correct my errors!

first, do a google on special characters to find the ±√ symbols, which you can then copy and paste. All those words are just too ugly for words! You have
y=2x^22x+1 and y=3x5, so set them equal:
2x^22x+1 = 3x5
2x^25x+6 = 0
The discriminant (b^24ac) is negative, so there are no solutions.
For the other,
y=x^2+3x16 and y=x^28x18
x^2+3x16 = x^28x18
2x^2+11x+2 = 0
the discriminant is positive, so it has two distinct solutions.
See the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3D2x^22x%2B1+%2C+y%3D+3x5
http://www.wolframalpha.com/input/?i=plot+y%3Dx^2%2B3x16+%2C+y%3Dx^28x18
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