Question Video: Finding the Solution Set of a Quadratic Equation Graphically | Nagwa Question Video: Finding the Solution Set of a Quadratic Equation Graphically | Nagwa

# Question Video: Finding the Solution Set of a Quadratic Equation Graphically Mathematics • Third Year of Preparatory School

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The graph shows the function π(π₯) = π₯Β² β 2π₯ + 3. What is the solution set of π(π₯) = 0?

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### Video Transcript

The graph shows the function π of π₯ equals π₯ squared minus two π₯ plus three. What is the solution set of π of π₯ equals zero.

Given some graph of a function π¦ equals π of π₯, the solutions to the equation π of π₯ equals zero correspond to the values of the π₯-intercepts if they exist. If there are no π₯-intercepts, it follows that there are no solutions to the equation π of π₯ equals zero. Now in this case, weβve been given the graph of the function π of π₯ equals π₯ squared minus two π₯ plus three and asked to solve π of π₯ equals zero or, in other words, π₯ squared minus two π₯ plus three equals zero.

But if we look carefully, we see that there are no locations where the graph, which is the green plot here, intersects the π₯-axis. And so, there are no real solutions to the equation π of π₯ equals zero. In order to use set notation, we need to find a way to show that there are no values inside the set. So we use the notation shown. Itβs the null set or empty set.

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