Q. 2 C

# Solve the following quadratic equations:(2 + i)x2 – (5 – i)x + 2(1 – i) = 0

(2 + i)x2 – (5 – i)x + 2(1 – i) = 0

Given (2 + i)x2 – (5 – i)x + 2(1 – i) = 0

Recall that the roots of quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by Here, a = (2 + i), b = –(5 – i) and c = 2(1 – i)   By substituting i2 = –1 in the above equation, we get    We can write –2i = –2i + 1 – 1

–2i = –2i + 1 + i2 [ i2 = –1]

–2i = 1 – 2i + i2

–2i = 12 – 2(1)(i) + i2

–2i = (1 – i)2 [ (a – b)2 = a2 – 2ab + b2]

By using the result –2i = (1 – i)2, we get          [ i2 = –1]   Thus, the roots of the given equation are 1 – i and .

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