SOLUTION: I am helping my son with his homework and i need answers to problems to confirm they are correct. Can you please show the work as well? Use the quadratic formula to solve the

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Question 701477: I am helping my son with his homework and i need answers to problems to confirm they are correct. Can you please show the work as well?
Use the quadratic formula to solve the following:
1. X^2 -4x -5=0
2. t^2+8t+19=0
3. 8w^2-8w+2=0
4. 4x^2-8x+1=0
Find the discriminant of the quadratic equation and give the number and type of solutions for the equation for the following:
1. x^2-8x+16=0
2. 8p^2+8p+3=0
3. 5x^2+20x+21=0
4. 8n^2-4n+2=5n-11
THANK YOU SO MUCH
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I am helping my son with his homework and i need answers to problems to confirm they are correct. Can you please show the work as well?
Use the quadratic formula to solve the following:
1. X^2 -4x -5=0
x = [4 +- sqrt(16-4*-5)]/2
x = [4 +- sqrt(36)]/2
x = [4+6]/2 or x = [4-6]/2
x = 5 or x = -1
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2. t^2+8t+19=0
x = [-8 +- sqrt(64-4*19)]/2
x = [-8 +- sqrt(-12)]/2
x = [-8 +- 2sqrt(3)i]/2
x = [-4+sqrt(3)i] or x = [-4-sqrt(3)i]
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3. 8w^2-8w+2=0
w = [8 +- sqrt(64-4*8*2)]/16
w = [8 +- sqrt(16)]/16
w = [8 +- 4]/16
w = 3/4 or x = 1/4
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4. 4x^2-8x+1=0
x = [8 +- sqrt(64-4*4*1)
x = [8 +- sqrt(48)]/8
x = [8 +- 4sqrt(3)]/8
x = 1+(1/2)sqrt(3) or x = 1 - (1/2)sqrt(3)
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Find the discriminant of the quadratic equation and give the number and type of solutions for the equation for the following:
1. x^2-8x+16=0
b^2-4ac = 8^2-4*16 = 0 ; 2 equal Real Number solutions
--------------------------
2. 8p^2+8p+3=0
b^2 - 4ac = 8^2-4*8*3 = -32 ; 2 Complex Number solutions
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3. 5x^2+20x+21=0
b^2 -4ac = 400-4*5*21 = 400-420 = -20 ; 2 complex Number solutions
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4. 8n^2-4n+2=5n-11 = 8n^2 -9n+13
b^2-4ac = 81-4*8*13 < 0 so 2 complex Number solutions
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Cheers,
Stan H.
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