WeBWorK using host: https://webwork.pcc.edu, format: simple, seed: 3497, course: orcca

Identify which of the items are quadratic equations.

The equation $2x^2+5x=7$ a quadratic equation.

The equation $5-2x=3$ a quadratic equation.

The equation $15-x^3=3x^2+9x$ a quadratic equation.

The equation $(x+3)(x-4)=0$ a quadratic equation.

The equation $x(x+1)(x-1)=0$ a quadratic equation.

The expression $x^2-5x+6$ a quadratic equation.

The equation $(2x-3)(x+5)=12$ a quadratic equation.

Solution

The equation $2x^2+5x=7$ is a quadratic equation. To write it in standard form, simply subtract $7$ from both sides.

The equation $5-2x=3$ is not quadratic. It is a linear equation.

The equation $15+x^3=3x^2+9x$ is not a quadratic equation because of the $x^3$ term.

The equation $(x+3)(x-4)=0$ is a quadratic equation. If we expand the left-hand side of the equation, we would get something in standard form.

The equation $x(x+1)(x-1)=0$ is not a quadratic equation. If we expanded the left-hand side of the equation, we would have an expression with an $x^3$ term, which automatically makes it not quadratic.

The expression $x^2-5x+6$ is not a quadratic equation; it’s not an equation at all. Instead, this is a quadratic expression.

The equation $(2x-3)(x+5)=12$ is a quadratic equation. Multiplying out the left-hand side, and subtracting $12$ form both sides, we would have a quadratic equation in standard form.