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Solve the following quadratic equations by factorization method: x2 + 10ix – 21 = 0 |
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Answer» x2 + 10ix – 21 = 0 Given x2 + 10ix – 21 = 0 ⇒ x2 + 10ix – 21 × 1 = 0 We have i2 = –1 ⇒ 1 = –i2 By substituting 1 = –i2 in the above equation, we get x2 + 10ix – 21(–i2) = 0 ⇒ x2 + 10ix + 21i2 = 0 ⇒ x2 + 3ix + 7ix + 21i2 = 0 ⇒ x(x + 3i) + 7i(x + 3i) = 0 ⇒ (x + 3i)(x + 7i) = 0 ⇒ x + 3i = 0 or x + 7i = 0 ∴ x = –3i or –7i Thus, the roots of the given equation are –3i and –7i. |
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