Determine the Nature of the Roots Using the Discriminant 0=-2x^2+3

$0 = - 2 x^{2} + 3$

Step 1

Move all the expressions to the left side of the equation.

Add $2 x^{2}$ to both sides of the equation.

$2 x^{2} = 3$

Subtract $3$ from both sides of the equation.

$2 x^{2} - 3 = 0$

Step 2

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

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

Step 3

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

$0^{2} - 4 (2 \cdot - 3)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$0 - 4 (2 \cdot - 3)$

Multiply $- 4 (2 \cdot - 3)$ .

Multiply $2$ by $- 3$ .

$0 - 4 \cdot - 6$

Multiply $- 4$ by $- 6$ .

$0 + 24$

Add $0$ and $24$ .

$24$

Step 5

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant $(Δ)$ :

$Δ > 0$ means there are $2$ distinct real roots.

$Δ = 0$ means there are $2$ equal real roots, or $1$ distinct real root.

$Δ < 0$ means there are no real roots, but $2$ complex roots.

Since the discriminant is greater than $0$ , there are two real roots.

Two Real Roots