Answer:
[tex]\boxed {\boxed {\sf 136}}[/tex]
Step-by-step explanation:
The quadratic formula helps us find the roots of a quadratic equation. The equation is:
[tex]\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} } \\ \end{array}[/tex]
where [tex]ax^2+bx+c=0[/tex]
The discriminant is just the part under the square root. This helps tell us if there are two, one, or zero real solutions.
The discriminant is:
[tex]b^2-4ac[/tex]
We are given the quadratic: [tex]9x^2-8x-2=0[/tex]
Therefore, a is 9, b is -8, and c is -2.
[tex]a=9 \\ b= -8 \\c= -2\\[/tex]
[tex](-8)^2-[4(9)(-2)][/tex]
Solve the exponent.
[tex]64-[4(9)(-2)][/tex]
Multiply 4, 9, and -2.
[tex]64-(-72) = 64+72 \\=136[/tex]
The discriminant is 136. Since it is a non-zero, positive number, this quadratic has 2 real solutions/zeroes/roots.
