Question

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation.

Answer 1

We are told to use the discriminant to determine whether the quadratic equation has two unequal real​ solutions, a repeated real​ solution, or no real​ solution, without solving the equation

`9x^2-7x+8=0`

The discriminant formula is given by

`d=b^2-4ac`

Where d is the discriminant.

If

`\begin{gathered} d>0,\text{ we have 2 real roots} \\ \\ d=0,we\text{ have 1 real root} \\ \\ d<0,we\text{ have 2 complex roots } \end{gathered}`

Now

`\begin{gathered} b^2-4ac \\ \\ -7^2-4*9*8 \\ \\ 49-288 \\ \\ =-239 \end{gathered}`

So, since our value for d < 0, the equation has 2 complex roots.

Therefore, the equation has no real solution

So, the last option is the correct answer.