Question

(1) Draw the graph of y = x² and y = 2x + 3 and hence solve the equation x² − 2x − 3 = 0.

(2) Draw the graph of y = 2x² and y = 3 − x and hence solve the equation 2x² + x − 3 = 0.

(3) Draw the graph of y = 2x² and y = 3 + x and hence solve the equation 2x² − x − 3 = 0.

Answer 1

(1) We need to solve the equations.

We make the following table for.

Plot the points (0, 0), (1, 1), (–1, 1), (2, 4) and (–2, 4) and join them smoothly

We make the following table for.

Plot the points (0, 3), (1, 5), (–1, 1), (2, 7) and (–2, –1) and join them.

From the intersection of the lineand the curve_, draw perpendiculars to the x-axis.

_{It can be noted that:}

Hence, the roots of are_.

(2) We need to solve the equations

We make the following table for.

Plot the points (0, 0), (1, 2), (–1, 2), (2, 8) and (–2, 8) and join them smoothly.

We make the following table for.

Plot the points (0, 3), (1, 2), (–1, 4), (2, 1) and (–2, 5) and join them.

From the intersection of the lineand the curve_, draw perpendiculars to the x-axis.

_{It can be noted that:}

Hence, the roots of are_.

(3) We need to solve the equations

We make the following table for.

Plot the points (0, 0), (1, 2), (–1, 2), (2, 8) and (–2, 8) and join them smoothly.

We make the following table for.

Plot the points (0, 3), (1, 4), (–1, 2), (2, 5) and (–2, 1) and join them.

From the intersection of the lineand the curve_, draw perpendiculars to the x-axis.

_{It can be noted that:}

Hence, the roots of are_.