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Definition of Functions

Solve : 2 +...

Question

Solve : $(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0$

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Solution

Given,

$(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0$

$(2 + i) {(a + b i)}^{2} - (5 - i) (a + b i) + 2 (1 - i) = 0$

$(2 a^{2} - 2 b^{2} - 2 a b - 5 a - b + 2) + i (- 2 + a + a^{2} - b^{2} - 5 b + 4 a b) = 0$

$(2 a^{2} - 2 b^{2} - 2 a b - 5 a - b + 2) + i (- 2 + a + a^{2} - b^{2} - 5 b + 4 a b) = 0 + 0 i$

$(2 a^{2} - 2 b^{2} - 2 a b - 5 a - b + 2) + i (- 2 + a + a^{2} - b^{2} - 5 b + 4 a b) = 0 + 0 i$

solving the above 2 equations, we get,

$(\begin{matrix} a = 1, & b = - 1 a = \frac{4}{5}, & b = - \frac{2}{5} \end{matrix})$

$x = 1 - i, \frac{4}{5} - \frac{2}{5} i$

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Similar questions

2 (1 + i) x^{2} - 4 (2 - i) x - 5 - 3 i = 0.

Solve the following quadratic equations :

(i) $x^{2} - (3 \sqrt{2} + 2 i) x + 6 \sqrt{2} i = 0$

(ii) $x^{2} - (5 - i) x + (18 + i) = 0$

(iii) $(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0$

(iv) $x^{2} - (2 + i) x - (1 - 7 i) = 0$

(v) $i x^{2} - 4 x - 4 i = 0$

(vi) $x^{2} + 4 i x - 4 = 0$

(vii) $2 x^{2} + \sqrt{15} i x - i = 0$

(viii) $x^{2} - x + (1 + i) = 0$

(ix) $i x^{2} - x + 12 i = 0$

(x) $x^{2} - (3 \sqrt{2} - 2 i) x - \sqrt{2} i = 0$

(xi) $x^{2} - (\sqrt{2} + i) x + \sqrt{2} i = 0$

(xii) $2 x^{2} - (3 + 7 i) x + (9 i - 3) = 0$

x^{2} - (3 \sqrt{2} + 2 i) x + 6 \sqrt{2 i} = 0

x^{2} - (5 - i) x + (18 + i) = 0

(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0

x^{2} - (2 + i) x - (1 - 7 i) = 0

i x^{2} - 4 x - 4 i = 0

x^{2} + 4 i x - 4 = 0

2 x^{2} + \sqrt{15} i x - i = 0

x^{2} - x + (1 + i) = 0

i x^{2} - x + 12 i = 0

x^{2} - (3 \sqrt{2} - 2 i) x - \sqrt{2} i = 0

x^{2} - (\sqrt{2} + i) x + \sqrt{2} i = 0

2 x^{2} - (3 + 7 i) x + (9 i - 3) = 0

x^{2} - (5 - i) x + (18 + i) = 0

i x^{2} - 2 (1 + i) x + (2 - i) = 0

(3 - i)

i = \sqrt{- 1}

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