Question

question 9 of 10
what is the discriminant of the polynomial below?
$2x^2 + 5x - 8$

a. -59

b. 89

c. -39

d. 31

Explanation:

Step1: Recall the discriminant formula

For a quadratic polynomial \( ax^{2}+bx + c \), the discriminant \( D \) is given by \( D=b^{2}-4ac \).

Step2: Identify \( a \), \( b \), and \( c \)

In the polynomial \( 2x^{2}+5x - 8 \), we have \( a = 2 \), \( b = 5 \), and \( c=-8 \).

Step3: Substitute into the formula

Substitute \( a = 2 \), \( b = 5 \), and \( c = - 8 \) into the discriminant formula:
\[

$$\begin{align*} D&=5^{2}-4\times2\times(-8)\\ &=25+64\\ &=89 \end{align*}$$

\]

Answer:

B. 89