Question

I just need to make sure 1-9 are correct so if you could confirm please.9 b)

Answer 1

Given:

`2x^2+3x+9=0`

To find:

The roots.

Step-by-step explanation:

Here,

`\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}`

Using the quadratic formula,

`x=(-b\pm√(b^2-4ac))/(2a)`

On substitution we get,

`\begin{gathered} x=(-3\pm√((3)^2-4(2)(9)))/(2(2)) \\ =(-3\pm√(9-72))/(4) \\ =(-3\pm√(-63))/(4) \\ =(-3\pm3i√(7))/(4) \end{gathered}`

Therefore, the solutions are,

`x=(-3+3\imaginaryI√(7))/(4),x=(-3-3\imaginaryI√(7))/(4)`

Final answer:

The solutions are,

`x=(-3+3\imaginaryI√(7))/(4),x=(-3-3\imaginaryI√(7))/(4)`