draw the graph of y=2x²and hence solve 2x²-x-6=0
Answers
Answer:
The correct option is B {-2, 1.5}
First, let us draw the graph of
y
=
2
x
2
.
x
−
3
−
2
−
1
0
1
2
3
x
2
9
4
1
0
1
4
9
y
=
2
x
18
8
2
0
2
8
18
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
2
x
2
+
x
−
6
=
0
, solve the two equations.
y
=
2
x
2
and
2
x
2
+
x
−
6
=
0
. Now,
2
x
2
+
x
−
6
=
0
.
⇒
y
+
x
−
6
=
0
, since
y
=
2
x
2
Thus,
y
=
−
x
+
6
Hence, the roots of
2
x
2
+
x
−
6
=
0
are nothing but the x-coordinates of the points of intersection of
y
=
2
x
2
and
y
=
−
x
+
6
.
Now, for the straight line
y
=
−
x
+
6
, from the following table.
x
−
1
0
1
2
y
=
−
x
+
6
7
6
5
4
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
2
x
2
+
x
−
6
=
0
is {-2, 1.5}.