Question

the discriminant of the equation -9x^2=-8x+8look at the picture for a better look at it

Answer 1

ANSWER

2 imaginary solutions.

EXPLANATION

The discriminant for a quadratic equation with the form,

$ax^2+bx+c=0$

Is,

$D=b^2-4ac$

And we have three possible outcomes,

$\begin{gathered} D>0\to2\text{ real solutions} \\ D=0\to1\text{ real solution} \\ D<0\to2\text{ imaginary solutions} \end{gathered}$

We can add 9x² from the given equation to write it in standard form,

$0=9x^2-8x+8$

Thus for this equation we have a = 9, b = -8 and c = 8. Find the discriminant,

$D=(-8)^2-4\cdot9\cdot8=64-288=-224<0$

The discriminant is less than zero, therefore, it has 2 imaginary solutions.