Determine the discriminant of $$ 0=2 x^{2}+4 x+10 $$

Question

UpStudy AI · Accepted Answer

1. The discriminant $$ \Delta $$ of a quadratic equation $$ ax^2 + bx + c = 0 $$ is given by:
   $$
   \Delta = b^2 - 4ac
   $$

2. For the equation $$ 0 = 2x^2 + 4x + 10 $$, we identify:
   $$
   a = 2, \quad b = 4, \quad c = 10
   $$

3. Substituting these values into the formula for the discriminant:
   $$
   \Delta = 4^2 - 4 \cdot 2 \cdot 10
   $$

4. Calculating the values:
   $$
   \Delta = 16 - 80
   $$

5. Simplifying, we find:
   $$
   \Delta = -64
   $$
The discriminant is -64.

Determine the discriminant of \( 0=2 x^{2}+4 x+10 \)