Question

Solve the given quadratic equation:
x² + 3ix + 10 = 0

Answer 1

To solve this equation, let us apply Quadratic formula

${x}^{2} +3ix + 10= 0 \\ \\ a = 1\\ \\ b = 3i \\ \\ c = 10 \\ \\ x_{1,2} = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_{1,2} = \frac{ -3i ± \sqrt{ {(-3i)}^{2} - 4(1)(10)} }{2 \times 1} \\ \\ x_{1,2} = \frac{ -3i ± \sqrt{-9 - 40} }{2} \\ \\ x_{1,2} = \frac{ -3i±\sqrt{ -49} }{2} \\ \\ \\ x_{1,2} = \frac{ -3i± 7i}{2} \\ \\ x_{1} = \frac{ 4i}{2} \\ \\x_{1} =2i\\\\ x_{2} = \frac{ -10i}{2} \\ \\x_{2} =-5i$
Hope it helps you.

Answer 2

Answer:

The solution of quadratic equation are 2i and -5i.              

Step-by-step explanation:

Given : Quadratic equation $x^2+ 3ix + 10 = 0$

To find : Solve the quadratic equation ?

Solution :

The general solution of quadratic equation $ax^2+bx+c=0$ is given by $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing, a=1 , b=3i and c=10

Substitute the values in the formula,

$x=\frac{-(3i)\pm\sqrt{(3i)^2-4(1)(10)}}{2(1)}$

$x=\frac{-3i\pm\sqrt{9(-1)-40}}{2}$

$x=\frac{-3i\pm\sqrt{-49}}{2}$

$x=\frac{-3i\pm7i}{2}$

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

$x=\frac{4i}{2},\frac{-10i}{2}$

$x=2i,-5i$

Therefore, The solution of quadratic equation are 2i and -5i.