1. If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes = _____
Q2 . The zero of the polynomial p(x) = ax +b is ______________
the zeroes are on the x-axis, right?
ax+b = 0
ax = -b
x = -b/a
1. If the graph of a polynomial intersects the x-axis at three points, then the number of zeroes is 3. This is because the x-intercepts represent the values of x for which the polynomial evaluates to 0, and each x-intercept corresponds to a zero of the polynomial.
2. To find the zero of the polynomial p(x) = ax + b, we set the polynomial equal to zero and solve for x.
ax + b = 0
To isolate x, we subtract b from both sides:
ax = -b
Finally, we divide both sides by a to solve for x:
x = -b/a
Therefore, the zero of the polynomial p(x) = ax + b is -b/a.
Q1. If the graph of a polynomial intersects the x-axis at three points, then the number of zeroes = 3.
To understand why, we need to know that the zeroes of a polynomial are the values of x for which the polynomial evaluates to zero. In other words, the zeroes are the x-coordinates of the points where the polynomial intersects the x-axis.
When a polynomial intersects the x-axis, it means that the y-coordinate of those points is zero. Since the y-coordinate represents the value of the polynomial, we can conclude that the polynomial evaluates to zero at those x-values.
In this case, if the graph of a polynomial intersects the x-axis at three points, it means that there are three x-values for which the polynomial evaluates to zero. Therefore, the number of zeroes of the polynomial is 3.
Q2. The zero of the polynomial p(x) = ax + b is -b/a.
To find the zero of a polynomial, we set the polynomial equal to zero and solve for x. In this case, we have the polynomial p(x) = ax + b.
Setting p(x) equal to zero, we get:
ax + b = 0
To solve this equation for x, we isolate x by moving b to the other side:
ax = -b
Now, divide both sides by a to solve for x:
x = -b/a
Therefore, the zero of the polynomial p(x) = ax + b is -b/a.