Question

Determine the number of solutions and place on the appropriate field in the table 5x^=4x

Answer 1

As given by the question

There are given that the equation

Now,

From the first equation

`5x^2+2=4x`

Solve the given equation by using quadratic formula to check the solution is imaginary or real.

So,

From the quadratic formula;

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

So,

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4*5*2}}{2*5} \\ x=\frac{4\pm2\sqrt[]{6}i}{2*5} \\ x=(2)/(5)+i\frac{\sqrt[]{6}}{5},\text{ }(2)/(5)+i\frac{\sqrt[]{6}}{5} \end{gathered}`

Hence, the value of the given equation is shown below:

`x=(2)/(5)+i\frac{\sqrt[]{6}}{5},\text{ }(2)/(5)+i\frac{\sqrt[]{6}}{5}`

So, there is No real solution.