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In this lesson, we will learn how to solve a cubic equation graphically.

Q1:

The figure shows the graphs of the curve π¦ = π₯ ( π₯ β 1 ) ( π₯ + 2 ) and the line π¦ = π ( π₯ β 1 ) for some π < 0 .

The graphs intersect at three points, one of which has π₯ -coordinate 1. Find a quadratic equation whose roots are the π₯ -coordinates of the other two points of intersection.

By considering the discriminant of this quadratic equation, find the slope of the line through ( 1 , 0 ) which is tangent to the curve at some other point.

At what point is this line tangent to the curve?

Q2:

Use technology to plot the graph of π ( π₯ ) = π₯ + 5 π₯ β 1 0 0 3 2 , and use this graph to find the solutions to the equation π₯ + 5 π₯ = 1 0 0 3 2 to two decimal places.

Q3:

Use technology to plot the graph of π ( π₯ ) = π₯ + 3 π₯ β 2 3 2 , and use this graph to find the solutions to the equation π₯ + 3 π₯ = 2 3 2 to two decimal places.

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