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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.

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 class=

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SOLUTION

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

[tex]9x^2-7x+8=0[/tex]

The discriminant formula is given by

[tex]d=b^2-4ac[/tex]

Where d is the discriminant.

If

[tex]\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}[/tex]

Now

[tex]\begin{gathered} b^2-4ac \\ \\ -7^2-4\times9\times8 \\ \\ 49-288 \\ \\ =-239 \end{gathered}[/tex]

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.

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