Find the Discriminant 5x^2+14x+9=0

$5 x^{2} + 14 x + 9 = 0$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of $a$ , $b$ , and $c$ .

$14^{2} - 4 (5 \cdot 9)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $14$ to the power of $2$ .

$196 - 4 (5 \cdot 9)$

Multiply $- 4 (5 \cdot 9)$ .

Multiply $5$ by $9$ .

$196 - 4 \cdot 45$

Multiply $- 4$ by $45$ .

$196 - 180$

Subtract $180$ from $196$ .

$16$