Solve the quadratic equation: ix2 – 4x – 4i = 0

1.	Solve the quadratic equation: ix2 – 4x – 4i = 0
Answer» Given as ix² – 4x – 4i = 0 ix² + 4x(–1) – 4i = 0 [as we know, i² = –1] Therefore by substituting –1 = i² in the above equation, we get ix² + 4xi² – 4i = 0 i(x² + 4ix – 4) = 0 x² + 4ix – 4 = 0 x² + 4ix + 4(–1) = 0 x² + 4ix + 4i² = 0 [Since, i² = –1] x² + 2ix + 2ix + 4i² = 0 x(x + 2i) + 2i(x + 2i) = 0 (x + 2i) (x + 2i) = 0 (x + 2i)² = 0 x + 2i = 0 x = –2i, -2i Therefore, the roots of the given equation are –2i, –2i

Answer»

Given as ix² – 4x – 4i = 0

ix² + 4x(–1) – 4i = 0 [as we know, i² = –1]

Therefore by substituting –1 = i² in the above equation, we get

ix² + 4xi² – 4i = 0

i(x² + 4ix – 4) = 0

x² + 4ix – 4 = 0

x² + 4ix + 4(–1) = 0

x² + 4ix + 4i² = 0 [Since, i² = –1]

x² + 2ix + 2ix + 4i² = 0

x(x + 2i) + 2i(x + 2i) = 0

(x + 2i) (x + 2i) = 0

(x + 2i)² = 0

x + 2i = 0

x = –2i, -2i

Therefore, the roots of the given equation are –2i, –2i

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