Find the Discriminant 7x^2-9x+4=0

$7 x^{2} - 9 x + 4 = 0$

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 $c$ .

${(- 9)}^{2} - 4 (7 \cdot 4)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 9$ to the power of $2$ .

$81 - 4 (7 \cdot 4)$

Multiply $- 4 (7 \cdot 4)$ .

Multiply $7$ by $4$ .

$81 - 4 \cdot 28$

Multiply $- 4$ by $28$ .

$81 - 112$

Subtract $112$ from $81$ .

$- 31$