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Solve the following Quadratic Equations using the Quadratic Formula

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Solve the following Quadratic Equations using the Quadratic Formula

asked Oct 6, 2018 in ALGEBRA 1 by anonymous

1 Answer

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3)
2x^2 - 4x - 1   =  0
Compare it to quadratic form ax^2 + bx + c  =  0
a = 2, b = -4, c = -1
Roots are  
x  =  [ - b ± √(b^2 - 4ac) ] / 2a
x  =  [ - (-4) ± √((-4)^2 - 4(2)(-1)) ] / 2(2)
x  =  [ 4  ± √(16 + 8) ] / 4
x  =  [ 4  ± √24 ] / 4
x  =  [ 4  ± 2√6 ] / 4
x  =  2[ 2  ± √6 ] / 4
x  =  (2  ± √6)/2
x  =  (2  + √6)/2     ;       x  =  (2  - √6)/2
4)
x(x - 3) + 1  =  0
x^2 - 3x + 1  =  0
Compare it to quadratic form ax^2 + bx + c  =  0
a = 1, b = -3, c = 1
Roots are  
x  =  [ - b ± √(b^2 - 4ac) ] / 2a
x  =  [ - (-3) ± √((3)^2 - 4(1)(1)) ] / 2(1)
x  =  [ 3 ± √(9 - 4) ] / 2
x  =  [ 3 ± √5 ] / 2
x  =  [ 3 + √5 ] / 2     ;      x  =  [ 3  - √5 ] / 2

5)

x^2 - 4x + 2   =  0
Compare it to quadratic form ax^2 + bx + c  =  0
a = 1, b = -4, c = 2
Roots are  
x  =  [ - b ± √(b^2 - 4ac) ] / 2a
x  =  [ - (-4) ± √((-4)^2 - 4(1)(2)) ] / 2(1)
x  =  [ 4 ± √(16 - 8)) ] / 2
x  =  [ 4 ± √8 ] / 2
x  =  [ 4 ± 2√2 ] / 2
x  =  2[ 2 ± √2 ] / 2
x  =   2 ± √2
x  =   2 + √2      ;       x  =   2 - √2
Answer :

3)  The Solutions are  x  =  (2  + √6)/2  and  x  =  (2  - √6)/2

4)  The Solutions are x  =  [ 3 + √5 ] / 2  and  x  =  [ 3  - √5 ] / 2

5)  The Solutions are  x  =   2 + √2  and   x  =   2 - √2.

 

answered Oct 10, 2018 by homeworkhelp Mentor
edited Oct 11, 2018 by bradely

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