Question

${3x}^{2} - 6x + 7 = 0$

guys do this by formula method.
lesson name : polynomials
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Answer 1

hi mate,

solution:

3x²-6x+7=0

Solving 3x²-6x+7 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax²+Bx+C = 0 ,

- B ± √ B²-4AC

x = ————————

2A

In our case, A = 3

B = -6

C = 7

Accordingly, B2 - 4AC =

36 - 84 =

-48

Applying the quadratic formula :

6 ± √ -48

x = —————

6

Accordingly,√ -48 =

√ 48 • (-1) =

√ 48 • √ -1 =

± √ 48 • i

√ 48 = √ 2•2•2•2•3 =2•2•√ 3 =

± 4 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 6 ± 4 • 1.732 i ) / 6

Two imaginary solutions :

x =(6+√-48)/6=1+2i/3√ 3 = 1.0000+1.1547i

or:

x =(6-√-48)/6=1-2i/3√ 3 = 1.0000-1.1547i

Two solutions were found :

x =(6-√-48)/6=1-2i/3√ 3 = 1.0000-1.1547i

x =(6+√-48)/6=1+2i/3√ 3 = 1.0000+1.1547i

i hope it helps you.