Question

13.Solve using the Quadratic Formula for 2x² – 3x + 5 = 0a.X=(3 : iV31)/4b. = (3 + 731)/4x = 3 + V3X =C.

Answer 1

`2x^2-3x+5=0`

The quadratic formula is:

`\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

For the given equation you have:

a=2

b=-3

c=5

`\begin{gathered} x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(5)}}{2(2)} \\ \\ x=\frac{3\pm\sqrt[]{9-40}}{4} \\ \\ x=\frac{3\pm\sqrt[]{-31}}{4} \end{gathered}`

For the square root of a negative number you have that:

`\sqrt[]{-1}=i`

Then:

`\sqrt[]{-31}=\sqrt[]{-1}\cdot\sqrt[]{31}=i\sqrt[]{31}`Then, the solution of the quadratic equation using the quadratic formula is:
`x=\frac{3\pm i\cdot\sqrt[]{31}}{4}`