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Solve the following quadratic equations by factorization method: 6x2 – 17ix – 12 = 0 |
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Answer» 6x2 – 17ix – 12 = 0 Given 6x2 – 17ix – 12 = 0 ⇒ 6x2 – 17ix – 12x1 = 0 We have i2 = –1 ⇒ 1 = –i2 By substituting 1 = –i2 in the above equation, we get 6x2 – 17ix – 12(–i2) = 0 ⇒ 6x2 – 17ix + 12i2 = 0 ⇒ 6x2 – 9ix – 8ix + 12i2 = 0 ⇒ 3x(2x – 3i) – 4i(2x – 3i) = 0 ⇒ (2x – 3i)(3x – 4i) = 0 ⇒ 2x – 3i = 0 or 3x – 4i = 0 ⇒ 2x = 3i or 3x = 4i x = \(\frac{3}{2}i,or\frac{4}{3}i\) Thus, the roots of the given equation are \(\frac{3}{2}i,or\frac{4}{3}i\) |
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