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

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

Move all terms to the left side of the equation and simplify.

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

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Move $2 x^{2}$ to the left side of the equation by adding it to both sides.

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

Move $3$ to the left side of the equation by subtracting it from both sides.

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

Add $0$ and $2 x^{2}$ .

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

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

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

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

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

Evaluate the result to find the discriminant.

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Simplify each term.

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

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

Multiply $2$ by $- 3$ .

$0 - 4 \cdot - 6$

Multiply $- 4$ by $- 6$ .

$0 + 24$

Add $0$ and $24$ .

$24$

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

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

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