Question

What are the solutions of 2x2- 6x+5=0?

Answer 1

Answer:

$x_{1}=\frac{3}{2}+\frac{i}{2}$

$x_{2}=\frac{3}{2}-\frac{i}{2}$

Step-by-step explanation:

It is a Quadratic Equation

$2x^2-6x+5=0$

Once it cannot be easily factored, you solve it using the quadratic formula or completing the square. I will use the quadratic formula.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot 2\cdot 5}}{2\cdot 2}$

The discriminant is negative, therefore we got complex solutions.

$\Delta= \sqrt{-4}= \sqrt{4i} =2i$

$x=\frac{6\pm 2i}{4}$

$x_{1}=\frac{3+i}{2}$

$x_{2}=\frac{3-i}{2}$

Now, just rewrite the roots in standard complex form

$x_{1}=\frac{3}{2}+\frac{i}{2}$

$x_{2}=\frac{3}{2}-\frac{i}{2}$