Question

Evaluate the expression. $$b^{2}-4 a c \text { when } a=1, b=3, \text { and } c=5$$

Short answer

-11

Step-by-step solution

Substitute the given values

Substitute \(a = 1\), \(b = 3\), and \(c = 5\) into the given expression \(b^{2} - 4ac\). The new expression becomes \(3^{2} - 4 \cdot 1 \cdot 5\).

Perform the operations

Perform the operations in the correct order according to the BIDMAS/BODMAS rule (Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction). We first conduct the exponentiation operation \(3^{2}\) giving us 9, followed by the multiplication \(4 \cdot 1 \cdot 5\), yielding 20. The expression now reads as \(9 - 20\).

Final calculation

We finish by performing the subtraction operation, giving us a final result of -11.