Questions: Evaluate the algebraic expression. b^2 - 4ac for a=5, b=8, and c=-5

Transcript text: Evaluate the algebraic expression. \[ b^{2}-4 a c \text { for } a=5, b=8, \text { and } c=-5 \]

Solution

Solution Steps

To evaluate the algebraic expression \( b^{2} - 4ac \), substitute the given values of \( a \), \( b \), and \( c \) into the expression. Then, perform the arithmetic operations: first calculate \( b^{2} \), then calculate \( 4ac \), and finally subtract the result of \( 4ac \) from \( b^{2} \).

Step 1: Substitute the Given Values

Substitute the given values \( a = 5 \), \( b = 8 \), and \( c = -5 \) into the expression \( b^2 - 4ac \).

Step 2: Calculate \( b^2 \)

Calculate \( b^2 \) as follows: \[ b^2 = 8^2 = 64 \]

Step 3: Calculate \( 4ac \)

Calculate \( 4ac \) as follows: \[ 4ac = 4 \times 5 \times (-5) = -100 \]

Step 4: Evaluate the Expression

Substitute the results from Steps 2 and 3 into the expression: \[ b^2 - 4ac = 64 - (-100) = 64 + 100 = 164 \]