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Solution of an Equation

Solving the f...

Question

Solving the following quadratic equations by factorization method:
(i) $x^{2} + 10 i x - 21 = 0$
(ii) $x^{2} + (1 - 2 i) x - 2 i = 0$
(iii) $x^{2} - (2 \sqrt{3} + 3 i) x + 6 \sqrt{3} i = 0$
(iv) $6 x^{2} - 17 i x - 12 = 0$

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Solution

$(i) x^{2} + 10 i x - 21 = 0 \Rightarrow x^{2} + 7 i x + 3 i x - 21 = 0 \Rightarrow x (x + 7 i) + 3 i (x + 7 i) = 0 \Rightarrow (x + 7 i) (x + 3 i) = 0 \Rightarrow (x + 7 i) = 0 or (x + 3 i) = 0 \Rightarrow x = - 7 i, - 3 i So, the roots of the given quadratic equation are - 3 i and - 7 i .$

$(ii) x^{2} + (1 - 2 i) x - 2 i = 0 \Rightarrow x^{2} + x - 2 i x - 2 i = 0 \Rightarrow x (x + 1) - 2 i (x + 1) = 0 \Rightarrow (x + 1) (x - 2 i) = 0 \Rightarrow (x + 1) = 0 or (x - 2 i) = 0 \Rightarrow x = - 1, 2 i So, the roots of the given quadratic equation are - 1 and 2 i .$

$(iii) x^{2} - (2 \sqrt{3} + 3 i) x + 6 \sqrt{3} i = 0 \Rightarrow x^{2} - 2 \sqrt{3} x - 3 i x + 6 \sqrt{3} i = 0 \Rightarrow x (x - 2 \sqrt{3}) - 3 i (x - 2 \sqrt{3}) = 0 \Rightarrow (x - 2 \sqrt{3}) (x - 3 i) = 0 \Rightarrow (x - 2 \sqrt{3}) = 0 or (x - 3 i) = 0 \Rightarrow x = 2 \sqrt{3}, 3 i So, the roots of the given quadratic equation are 2 \sqrt{3} and 3 i .$

$(iv) 6 x^{2} - 17 i x - 12 = 0 \Rightarrow 6 x^{2} - 9 i x - 8 i x - 12 = 0 \Rightarrow 3 x (2 x - 3 i) - 4 i (2 x - 3 i) = 0 \Rightarrow (2 x - 3 i) (3 x - 4 i) = 0 \Rightarrow (2 x - 3 i) = 0 or (3 x - 4 i) = 0 \Rightarrow x = \frac{3}{2} i, \frac{4}{3} i So, the roots of the given quadratic equation are \frac{3}{2} i and \frac{4}{3} i .$

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Similar questions

Solve the following quadratic equations by factorization method :

(i) $x^{2} + 10 i x - 21 = 0$

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

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

(iv) $6 x^{2} - 17 i x - 12 = 0$

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} - 5 i x - 6 = 0

x^{2} + 4 i x - 4 = 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} - (3 \sqrt{2} + 2 i) x + 6 \sqrt{2 i} = 0

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