solve x²–2x+3=0 by using the quadratic formula
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x²-2x+3
a= 1,b= -2 and c =3
quadratic formula to find roots:
x=-b±√b²-4ac/2a
=>x=-(-2)±√(-2)²-4(1)(3)/2(1)
=>x=2±√(-2)²-4(1)(3) / 2
=>x= 2±√4-12 / 2
=>2 ± √ -8 / 2
The discriminant b²-4ac is less than 0
so,there are two complex roots.
√8 can also be written as√ 2×2×2= 2√2
=>x= 2±√-8 / 2
we use iota ( i ) in place of -ve value inside roots.
=>x= 2±2√2i / 2
simplify the term
=>x = 2/2 ± 2√2i /2
=>x= 1 ± √2i
=>x= 1+1.41421 i
=>x= 1-1.41421 i
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