Question

Draw the graph of $y=x^2-x-8$ and hence, solve the equation $x^2-2x-15=0$

Answer 1

First, let us draw the graph of $y=x^2-x-8$.

Now, let us assign integer values in the following table.

$\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ y& -2& -6& -8& -8& -6\end{array}$

Plot the points on the graph sheet

Scale: x-axis 1 cm = 2 units; y-axis 1 cm = 2 units

The curve, thus obtained is the graph of parabola $y=x^2-x-8$ and $x^2-2x-15=0$

Now, by solving the equations $x^2-2x-15=0$and $x^2-2x-15=0$

We get, y = x +7

y = x + 7 is a straight line. Consider the following table.

$$\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ y& 5& 6& 7& 8& 9\end{array}$$

The points of intersection of the parabola and the straight line are (-3,4) and (5,12)

The x – coordinates are -3 and 5.

Hence, the solution set of the equation $x^2-2x-15=0$ is {-3,5}