By using the method of completing …

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Yogita Ingle 6 years, 1 month ago
2x² + x + 4 = 0
(Divide by 2 through)
x² + 1/2x + 2 = 0
(Subtract 2 from both sides)
x² + 1/2x = -2
(add (b/2)² to both sides)
x² + 1/2x + (1/4)² = -2 + (1/4)²
(Complete the square)
(x + 1/4)² = -31/16
(Square root both sides)
x + 1/4 = ±√(-31/16)
x + 1/4 = ±i√(31/16)
Subtract 1/4 from both sides:
x = i√(31/16) - 1/4 or - i√(31/16) - 1/4
=> Both roots are imaginary numbers
=> There is no real roots
.
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