Consider a linear polynomial $ax + b$, $a ≠ 0$.
the graph of $y = ax + b$ is a straight line. For example, the graph of $y = 2x + 3$ is a straight line passing through the points (– 2, –1) and (1, 5).
(-2,-1)
(1,5)
$-3/2$
Geometrical Meaning of the Zeroes of a Polynomial
Please click the solve button for animation
the graph of $y = 2x + 3$ intersects the $x$ -axis mid-way
between $x = –1$ and $x = – 2$, that is, at the point ${-3/2}$
Thus we know that the zero of $2x + 3$ is ${-3/2}$ Thus, the zero of the polynomial $2x + 3$ is the x-coordinate of the point where the graph of $y = 2x + 3$ intersects the x-axis.
In general, 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, ${-b/a}$ Therefore, the linear polynomial $ax + b$, $a ≠ 0$, has exactly one zero, namely, the x-coordinate of the point where the graph of $y = ax + b$ intersects the x-axis.
Thus we know that the zero of $2x + 3$ is ${-3/2}$ Thus, the zero of the polynomial $2x + 3$ is the x-coordinate of the point where the graph of $y = 2x + 3$ intersects the x-axis.
In general, 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, ${-b/a}$ Therefore, the linear polynomial $ax + b$, $a ≠ 0$, has exactly one zero, namely, the x-coordinate of the point where the graph of $y = ax + b$ intersects the x-axis.