Find the Discriminant 1/2x^2+x-1=0

$\frac{1}{2} x^{2} + x - 1 = 0$

Step 1

Simplify the left side.

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} + x - 1 = 0$

Step 2

Multiply through by the least common denominator $2$ , then simplify.

Apply the distributive property.

$2 (\frac{x^{2}}{2}) + 2 x + 2 \cdot - 1 = 0$

Simplify.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (\frac{x^{2}}{2}) + 2 x + 2 \cdot - 1 = 0$

Rewrite the expression.

$x^{2} + 2 x + 2 \cdot - 1 = 0$

Multiply $2$ by $- 1$ .

$x^{2} + 2 x - 2 = 0$

Step 3

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

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

Step 4

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

$2^{2} - 4 (1 \cdot - 2)$

Step 5

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (1 \cdot - 2)$

Multiply $- 4 (1 \cdot - 2)$ .

Multiply $- 2$ by $1$ .

$4 - 4 \cdot - 2$

Multiply $- 4$ by $- 2$ .

$4 + 8$

Add $4$ and $8$ .

$12$