Formulas for complex numbers and quadratic equations 1
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27x² - 10x +1 = 0
find discriminant
D = b² - 4ac
= (-10)² - 4.27.1
= 100 - 108 = -8 < 0
Here D < 0 . it means given polynomial have no real roots .
Hence, we use the concept of complex number.
We know ,
i² = -1 use it here,
27x² -10x +1 = 0
Use quadratic formula ,
x = { -b ± √D}/2a
x = { 10 ± √(-8)}/2.27
= { 10 ± i2√2}/54
= (5 ±i√2)/27
Here, (5 +i√2)/27 , (5 -i√2)/27 are the real roots .
find discriminant
D = b² - 4ac
= (-10)² - 4.27.1
= 100 - 108 = -8 < 0
Here D < 0 . it means given polynomial have no real roots .
Hence, we use the concept of complex number.
We know ,
i² = -1 use it here,
27x² -10x +1 = 0
Use quadratic formula ,
x = { -b ± √D}/2a
x = { 10 ± √(-8)}/2.27
= { 10 ± i2√2}/54
= (5 ±i√2)/27
Here, (5 +i√2)/27 , (5 -i√2)/27 are the real roots .
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