The geometrical representation of the Polynomial p(x)=ax^2+bx+c is a shape called “Parabola” as geometrical representation of linear polynomial is a straight line.
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Let’s look at a linear polynomial ax + b, where a ≠ 0. You have already studied that the graph of y = ax + b is a straight line. Let’s look at the graph of y = 2x + 3.
x -2 2
y = 2x + 3 -1 7
The straight line y = 2x + 3 will pass through the points (- 2, – 1) and (2, 7). Here is how the graph looks like:
zeros
Fig. 1
From the Fig.1 above, you can see that the graph of y = 2x + 3 intersects the x-axis at the point (- 3/2, 0). Now, the zero of (2x + 3) is (- 3/2). Therefore, the zero of the linear polynomial (2x + 3) is the x-coordinate of the point where the graph of y = 2x + 3 intersects the x-axis. Hence, we can say,
For a linear polynomial ax + b, a ≠ 0, the graph of y = ax + b is a straight line which intersects the x-axis at exactly one point, namely, (- b/a, 0). Also, this linear polynomial has only one zero which is the x-coordinate of the point where the graph of y = ax + b intersects the x-axis.