Q. 2 D5.0( 3 Votes )

# Solve the following quadratic equations:x2 – (2 + i)x – (1 – 7i) = 0

x2 – (2 + i)x – (1 – 7i) = 0

Given x2 – (2 + i)x – (1 – 7i) = 0

Recall that the roots of quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by Here, a = 1, b = –(2 + i) and c = –(1 – 7i)    By substituting i2 = –1 in the above equation, we get  We can write 7 – 24i = 16 – 9 – 24i

7 – 24i = 16 + 9(–1) – 24i

7 – 24i = 16 + 9i2 – 24i [ i2 = –1]

7 – 24i = 42 + (3i)2 – 2(4)(3i)

7 – 24i = (4 – 3i)2 [ (a – b)2 = a2 – b2 + 2ab]

By using the result 7 – 24i = (4 – 3i)2, we get      x = 3 – i or –1 + 2i

Thus, the roots of the given equation are 3 – i and –1 + 2i.

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