Questions: a<0 ; b^2-4ac=0

Transcript text: $a<0 ; b^{2}-4 a c=0$

Solution

Solution Steps

To solve the given mathematical conditions, we need to check if the quadratic equation $ b^2 - 4ac = 0 $ holds true and if $ a < 0 $. This involves evaluating the given expressions and verifying the conditions.

Step 1: Verify $ a < 0 $

Given $ a = -1 $, we need to check if $ a < 0 $.

Since $ -1 < 0 $, the condition $ a < 0 $ is satisfied.

Step 2: Verify $ b^2 - 4ac = 0 $

Given $ b = 2 $, $ a = -1 $, and $ c = 1 $, we need to check if $ b^2 - 4ac = 0 $.

Calculate $ b^2 - 4ac $: \[ b^2 - 4ac = 2^2 - 4(-1)(1) = 4 + 4 = 8 \]

Since $ 8 \neq 0 $, the condition $ b^2 - 4ac = 0 $ is not satisfied.

Final Answer

$\boxed{8 \neq 0}$

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