Questions: What is the discriminant of the polynomial below? 2x^2 + 5x - 8 A. -59 B. 89 C. 31 D. -39

Solution Steps

To find the discriminant of a quadratic polynomial \( ax^2 + bx + c \), we use the formula \( b^2 - 4ac \). Here, \( a = 2 \), \( b = 5 \), and \( c = -8 \). We will substitute these values into the formula to calculate the discriminant.

For the quadratic polynomial \( 2x^2 + 5x - 8 \), we identify the coefficients:

• \( a = 2 \)
• \( b = 5 \)
• \( c = -8 \)

The discriminant \( D \) is calculated using the formula: \[ D = b^2 - 4ac \]

Substituting the identified coefficients into the formula: \[ D = 5^2 - 4 \cdot 2 \cdot (-8) \]

Calculating each part: \[ D = 25 - (-64) = 25 + 64 = 89 \]

Final Answer