Solve the following quadratic equations: ix2 – x + 12i = 0

1.	Solve the following quadratic equations: ix2 – x + 12i = 0
Answer» ix² – x + 12i = 0 Given ix² – x + 12i = 0 ⇒ ix²+ x(–1) + 12i = 0 We have i² = –1 By substituting –1 = i² in the above equation, we get ix²+ xi² + 12i = 0 ⇒ i(x² + ix + 12) = 0 ⇒ x² + ix + 12 = 0 ⇒ x²+ ix – 12(–1) = 0 ⇒ x² + ix – 12i² = 0 [∵ i² = –1] ⇒ x²– 3ix + 4ix – 12i² = 0 ⇒ x(x – 3i) + 4i(x – 3i) = 0 ⇒ (x – 3i)(x + 4i) = 0 ⇒ x – 3i = 0 or x + 4i = 0 ∴ x = 3i or –4i Thus, the roots of the given equation are 3i and –4i.

Answer»

ix² – x + 12i = 0

Given ix² – x + 12i = 0

⇒ ix²+ x(–1) + 12i = 0

We have i² = –1

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

ix²+ xi² + 12i = 0

⇒ i(x² + ix + 12) = 0

⇒ x² + ix + 12 = 0

⇒ x²+ ix – 12(–1) = 0

⇒ x² + ix – 12i² = 0 [∵ i² = –1]

⇒ x²– 3ix + 4ix – 12i² = 0

⇒ x(x – 3i) + 4i(x – 3i) = 0

⇒ (x – 3i)(x + 4i) = 0

⇒ x – 3i = 0 or x + 4i = 0

∴ x = 3i or –4i

Thus, the roots of the given equation are 3i and –4i.

Discussion