Question 64·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Given the equation $(x - 6)(x + 1)(x - 2)=0$ , what is the least positive solution of the equation?

A zero-product equation has factors multiplied together to make $0$ . In Desmos, graph the product and $y=0$ ; each intersection’s $x$ -coordinate is a solution. Find all the solutions before applying least positive. The leftmost solution might be negative, and another positive solution might be too large.

Hints

Hint 1
A factor is one expression being multiplied. If any factor is $0$ , the whole product is $0$ . On a graph of the product, where would its height be zero?
Hint 2
An $x$ -intercept is where a graph reaches height $0$ . Read the $x$ -coordinate at each intercept, then compare only the coordinates greater than $0$ .

Step-by-step

Graph the product and compare its solutions
Step 1
Connect solutions to the graph
The given product equals $0$ , so a value of $x$ solves the equation if it makes the product $0$ . On the product’s graph, that happens at an $x$ -intercept, where the graph reaches height $y=0$ .
Step 2
Read every solution, then choose
Type $y=(x-6)(x+1)(x-2)$ and $y=0$ in Desmos. Click their intersections: Desmos shows $(-1,0)$ , $(2,0)$ , and $(6,0)$ . The $x$ -coordinates are the solutions. $-1$ is negative, and $2<6$ , so the least positive solution is $2$ . Choice B.

Question 64·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this