Q. 2 D5.0( 3 Votes )

# Solve the following quadratic equations:

x^{2} – (2 + i)x – (1 – 7i) = 0

Answer :

x^{2} – (2 + i)x – (1 – 7i) = 0

Given x^{2} – (2 + i)x – (1 – 7i) = 0

**Recall that the roots of quadratic equation ax ^{2} + bx + c = 0, where a ≠ 0, are given by**

Here, a = 1, b = –(2 + i) and c = –(1 – 7i)

By substituting i^{2} = –1 in the above equation, we get

We can write 7 – 24i = 16 – 9 – 24i

⇒ 7 – 24i = 16 + 9(–1) – 24i

⇒ 7 – 24i = 16 + 9i^{2} – 24i [∵ i^{2} = –1]

⇒ 7 – 24i = 4^{2} + (3i)^{2} – 2(4)(3i)

⇒ 7 – 24i = (4 – 3i)^{2} [∵ (a – b)^{2} = a^{2} – b^{2} + 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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