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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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6)
4x^2  =  -2x + 1
4x^2 + 2x - 1  =  0
Compare it to quadratic form ax^2 + bx + c  =  0
a = 4, b = 2, c = -1
Roots are  
x  =  [ - b ± √(b^2 - 4ac) ] / 2a
x  =  [ - (2) ± √((2)^2 - 4(4)(-1)) ] / 2(4)
x  =  [ - (2) ± √(4 + 16) ] / 8
x  =  [ - 2  ± √20 ] / 8
x  =  [ - 2  ± 2√5 ] / 8
x  =  2[ - 1  ± √5 ] / 8
x  =  [ - 1  ± √5 ] / 4
x  =  [ - 1  + √5 ] / 4     ;       x  =  [ - 1  - √5 ] / 4
7)
 
x^2 - √3x + 3   =  0
Compare it to quadratic form ax^2 + bx + c  =  0
a = 1, b = -√3, c = 3
Roots are  
x  =  [ - b ± √(b^2 - 4ac) ] / 2a
x  =  [ - (-√3) ± √(3 - 4(1)(3)) ] / 2(1)
x  =  [ √3  ± √(3 - 12) ] / 2
x  =  [ √3  ± √(-9) ] / 2
x  =  [ √3  ± 3i ] / 2
x  =  [ √3  + 3i ] / 2      ;       x  =  [ √3  - 3i ] / 2
x  =  (√3)/2  + 3i/2     ;       x  =  (√3)/2  - 3i/2

Answer :

6)  The Solutions are  x  =  [ - 1  + √5 ] / 4  and  x  =  [ - 1  - √5 ] / 4

7)  The Solutions are  x  =  (√3)/2  + 3i/2  and  x  =  (√3)/2  - 3i/2.

answered Oct 10, 2018 by homeworkhelp Mentor

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