Solve the quadratic equation : $x^{2} + 3 i x + 10 = 0$

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Solution

Roots for the quadratic equation $a x^{2} + b x + c$ , the roots are
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

For the given equation $x^{2} + 3 i x + 10$ ,

$b^{2} - 4 a c = (3 i)^{2} - 4 (1) (10)$

$= 9 i^{2} - 40$

$= - 9 - 40 = - 49$

So, the roots are
$x = \frac{- 3 i \pm \sqrt{- 49}}{2}$

$x = \frac{- 3 i \pm 7 i}{2}$

$x = - 5 i, 2 i$

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

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

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

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

6 x^{2} - 17 i x - 12 = 0

x^{2} - 7 x + 10 = 0

x^{2} - 196 = 0

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