Answer:

QUADRATIC EQUATION

Direction: Determine the discriminant of x²-8x-1=0 and the nature of roots.

Final Answer:

Discriminant: 68

Nature of roots: real, irrational, and unequal

Step-by-step explanation:

x² - 8x - 1 = 0

First, identify the value of a, b, and c.

Given:

a = 1

b = -8

c = -1

Second, write the formula.

Formula to be used: \: \bold{ {b}^{2} - 4ac}b

2

−4ac

Lastly, solve using the formula then identify its nature of roots.

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} {b}^{2} - 4ac \\ {(-8)}^{2} - 4(1)(-1) \\ 64 + 4 \\ 68 \end{gathered} \end{gathered} \end{gathered} \end{gathered} \end{gathered}

b

2

−4ac

(−8)

2

−4(1)(−1)

64+4

68

Thus, the discriminant is 68 and the nature of roots is real, irrational, and unequal.