Question

14. Solve the equation 2x² – 4x + 3 = 0 using the quadratic formula.

Answer 1

`x=1+\frac{\sqrt[]{2}}{2}i;x=1-\frac{\sqrt[]{2}}{2}i`

Step-by-step explanation

We want to solve the given equation using the quadratic formula:

`2x^(2)-4x+3=0`

The quadratic formula is:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where a is the coefficient of x², b is the coefficient of x and c is the constant term.

Therefore, we have that:

`\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(2)(3)}}{2(2)} \\ x=\frac{4\pm\sqrt[]{16-24}}{4} \\ x=\frac{4\pm\sqrt[]{(-8)}}{4} \\ x=\frac{4\pm2\sqrt[]{2}i}{4} \\ \Rightarrow x=1+\frac{\sqrt[]{2}}{2}i;x=1-\frac{\sqrt[]{2}}{2}i \end{gathered}`

That is the solution of the equation.