Find the discriminant $$ -x^{2}-6 x+3 $$

Question

UpStudy AI · Accepted Answer

Let the quadratic expression be 
$$
- x^2 - 6x + 3.
$$

**Step 1: Identify the coefficients.**  
The standard form of a quadratic is 
$$
ax^2 + bx + c.
$$
For the given expression, we have:
$$
a = -1, \quad b = -6, \quad c = 3.
$$

**Step 2: Write the formula for the discriminant.**  
The discriminant $$ \Delta $$ of a quadratic is given by:
$$
\Delta = b^2 - 4ac.
$$

**Step 3: Substitute the values.**  
Substitute $$ a = -1 $$, $$ b = -6 $$, and $$ c = 3 $$:
$$
\Delta = (-6)^2 - 4(-1)(3).
$$

**Step 4: Compute the values.**  
First, compute $$ (-6)^2 $$:
$$
(-6)^2 = 36.
$$
Next, compute the product $$ -4(-1)(3) $$:
$$
-4(-1)(3) = 12.
$$
Thus, the discriminant becomes:
$$
\Delta = 36 + 12.
$$

**Step 5: Calculate the final result.**
$$
\Delta = 48.
$$

The discriminant is $$ \Delta = 48 $$.
The discriminant is 48.

Find the discriminant

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