Write the quadratic equation whose one root is: 1 − i.

1.	Write the quadratic equation whose one root is: 1 − i.
Answer» Since complex roots occurs in pair. The roots of quadratic equation are 1 − i and 1 + i Sum of roots = 1 − i + 1 + i = 2 Product of roots = (1 − i) (1 + i) = 1−i² = 1− (−1) = 2 Required quadratic equation: x²− (Sum of roots)x + (Product of roots) = 0 ⇒ x²− 2x + 2 = 0

Answer»

Since complex roots occurs in pair. The roots of quadratic equation are 1 − i and 1 + i

Sum of roots = 1 − i + 1 + i = 2

Product of roots = (1 − i) (1 + i) = 1−i²

= 1− (−1) = 2

Required quadratic equation:

x²− (Sum of roots)x + (Product of roots) = 0

⇒ x²− 2x + 2 = 0

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Write the quadratic equation whose one root is: 1 − i.

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