Explanation:

QUADRATIC EQUATION

Direction: Determine the nature of the roots of the following quadratic equation using the discriminant 2x²-10x+8=0.

Final Answer:

Discriminant: 36

Nature of roots: real, rational, and unequal

Step-by-step explanation:

2x² - 10x + 8 = 0

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

Given:

a = 2

b = -10

c = 8

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} {b}^{2} - 4ac \\ {(-10)}^{2} - 4(2)(8) \\ 10 - 64 \\ 36\end{gathered}

b

2

−4ac

(−10)

2

−4(2)(8)

10−64

36

Thus, the discriminant is 36 and the nature of roots is real, rational, and unequal.