Question

solve x²-4x+13 by factorisation method.

Answer 1

Correct Question :

Solve the equation x² - 4x + 13 = 0 by factorisation method .

AnswEr:

We have,

$\qquad \tt {x}^{2} - 4x + 13 = 0 \\ \\ \\ \implies \tt {x}^{2} - 4x + 4 + 9 = 0 \\ \\ \\ \implies \tt {(x - 2)}^{2} + 9 = 0 \\ \\ \\ \implies \tt {(x - 2)}^{2} - 9 {i}^{2} = 0 \\ \\ \\ \implies \tt {(x - 2)}^{2} - {(3i)}^{2} = 0 \\ \\ \\ \implies \tt \: [(x - 2) - 3i] \: [(x - 2) + 3i] = 0 \\ \\ \\ \implies \tt(x - 2 - 3i)(x - 2 + 3i) = 0 \\ \\ \\ \implies \tt \: x - 2 - 3i = 0 \: , \: or \: x - 2 + 3i = 0 \\ \\ \\ \implies \tt \: x = 2 + 3i \: , \: or \: \: x = 2 - 3i$

Hence, the roots of the given equation are 2 + 3i and 2 - 3i.