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### Theory:

Let us learn how to solve $$2$$ quadratic equations graphically.
Example:
1. Draw the graph of $$y = x^2 + 2x - 3$$ and hence solve $$x^2 - x - 6 = 0$$.

Solution:

Step 1: Draw the graph of the equation $$y = x^2 + 2x - 3$$.

The table of values for the equation $$y = x^2 + 2x - 3$$ is given by:

 $$x$$ $$-4$$ $$-3$$ $$-2$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$y$$ $$5$$ $$0$$ $$-3$$ $$-4$$ $$-3$$ $$1$$ $$5$$

Step 2: To solve the equation $$x^2 - x - 6 = 0$$, subtract the equation $$x^2 - x - 6 = 0$$ from $$y = x^2 + 2x - 3$$.

$$y = x^2 + 2x - 3$$

$$0 = x^2 - x - 6$$  ($$-$$)
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$$y = x + 3$$
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Step 3: Draw the graph of the equation $$y = x + 3$$.

The table of values for the equation $$y = x + 3$$ is given by:

 $$x$$ $$-4$$ $$-3$$ $$-2$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$3$$ $$y$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$

Step 4: Mark the points of intersection of $$y = x^2 + 2x - 3$$ and $$y = x + 3$$. The point of intersection is $$(-3,0)$$ and $$(2,5)$$.

Step 5: The $$x$$ - coordinates of the points are $$-3$$ and $$2$$. Therefore, the solution set for the equation $$x^2 - x - 6 = 0$$ is $${-3,2}$$.

2. Draw the graph of $$y = 2x^2 + x - 2$$ and hence solve $$2x^2 = 0$$.

Step 1: Draw the graph of the equation $$y = 2x^2 + x - 2$$.

The table of values for the equation $$y = 2x^2 + x - 2$$ is given by:

 $$x$$ $$-2$$ $$0$$ $$2$$ $$y$$ $$4$$ $$-2$$ $$8$$

Step 2: To solve the equation $$2x^2 = 0$$, subtract $$2x^2 = 0$$ from $$y = 2x^2 + x - 2$$.

$$y = 2x^2 + x - 2$$

$$0 = 2x^2$$             ($$-$$)
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$$y = x - 2$$
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Step 3: Draw the graph of the equation $$y = x - 2$$.

The table of values for the equation $$y = x - 2$$ is given by:

 $$x$$ $$-2$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$3$$ $$y$$ $$-4$$ $$-3$$ $$2$$ $$-1$$ $$0$$ $$1$$

Step 4: Mark the points of intersection of $$y = 2x^2 + x - 2$$ and $$y = x - 2$$. The point of intersection is $$(0,-2)$$.

Step 5: The $$x$$ - coordinates of the points is $$0$$. Therefore, the solution set for the equation $$2x^2 = 0$$ is $$0$$.