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Question


Draw the graph of 𝑦=(𝑥−1)(𝑥+3) and hence solve x2x6=0.


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Solution


Idea: To solve the quadratic equation, we need to find the equation of the line that cuts the parabola.

y = (x 1)(x + 3) = x2 x + 3x 3 = 0 y = x2+ 2x 3

Draw the parabola using the points (-4, 5), (-3, 0), (-2, -3), (-1,-4), (0, -3), (1, 0), (2, 5), (3, 12), (4, 21)
We can obtain the equation of a straight line by subtracting the equation given to solve from the equation of parabola. To solve the equation x2 x 6 = 0, subtract x2 x 6 = 0 from y = x2 2x 3

Plotting the points (-2, -3), (-1, 0), (0, 3), (2, 9), we get a straight line.

The points of intersection of the parabola with the straight line gives the roots of the equation.

The co-ordinates of the points of intersection forms the solution set.

∴ Solution {-2, 3}.


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