Question

Draw the graph of $y=2x^2$ and hence solve $2x^2+x-6=0$ .

• A. {2, 1.5}
• B. {-2, 1.5}
• C. {2, -1.5}
• D. {-2, -1.5}

Answer 1

The correct option is B {-2, 1.5}

First, let us draw the graph of $y=2x^2$.
$\begin{array}{cccccccc}x& -3& -2& -1& 0& 1& 2& 3\\ x^2& 9& 4& 1& 0& 1& 4& 9\\ y=2x& 18& 8& 2& 0& 2& 8& 18\end{array}$
Plot the points (-3, 18), (-2, 8), (-1, 2) (0, 0), (1, 2), (2, 8), (3, 18).
Draw the graph by joining the points by a smooth curve.
To find the roots of $2x^2+x-6=0$, solve the two equations.
$y=2x^2$ and $2x^2+x-6=0$. Now, $2x^2+x-6=0$.
$\Rightarrow y+x-6=0$, since $y=2x^2$ Thus, $y=-x+6$
Hence, the roots of $2x^2+x-6=0$ are nothing but the x-coordinates of the points of intersection of $y=2x^2$ and $y=-x+6$.
Now, for the straight line $y=-x+6$, from the following table.
$\begin{array}{ccccc}x& -1& 0& 1& 2\\ y=-x+6& 7& 6& 5& 4\end{array}$
Draw the straight line by joining the above points.
The points of intersection of the line and the parabola are (-2, 8) and (1.5, 4.5). The x-coordinates of the points are -2 and 1.5.
Thus, the solution set for the equation $2x^2+x-6=0$ is {-2, 1.5}.