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A polynomial's zeros can be represented graphically. The number of polynomial zeros equals the number of points on the graph of the polynomial
  • a)
    Intersects y-axis
  • b)
    Intersects x-axis
  • c)
    Intersects y-axis or x-axis
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
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A polynomials zeros can be represented graphically. The number of poly...
Explanation:

The correct answer is option 'B' - "Intersects x-axis".

To understand why this is the correct answer, let's first define what a polynomial zero is. In algebra, a zero of a polynomial function is a value of the variable that makes the polynomial equal to zero. In other words, it is a value of 'x' that satisfies the equation f(x) = 0.

Now, let's consider the graph of a polynomial function. The graph of a polynomial is a smooth curve that can intersect the x-axis at various points. Each point of intersection represents a value of 'x' for which the polynomial is equal to zero, i.e., a zero of the polynomial.

Graphical Representation:

When we graph a polynomial function, the x-axis represents the values of 'x', and the y-axis represents the corresponding values of the polynomial function, f(x).

Number of Polynomial Zeros:

The number of polynomial zeros is equal to the number of points where the graph of the polynomial intersects the x-axis. This is because these points represent the values of 'x' for which the polynomial is equal to zero.

Intersects Y-Axis:

The y-axis is the vertical line on the graph where x = 0. It is essential to note that the y-axis does not represent the values of 'x'. Therefore, the points where the graph intersects the y-axis do not correspond to the zeros of the polynomial. Instead, they represent the constant term or the y-intercept of the polynomial function.

Intersects X-Axis:

The x-axis is the horizontal line on the graph where y = 0. The points where the graph intersects the x-axis represent the values of 'x' for which the polynomial is equal to zero. Therefore, these points correspond to the zeros of the polynomial function.

Intersects Y-Axis or X-Axis:

The option 'C' incorrectly suggests that the number of polynomial zeros is equal to the number of points where the graph intersects either the y-axis or the x-axis. As explained earlier, the points of intersection with the y-axis do not correspond to the zeros of the polynomial. Therefore, this option is incorrect.

None of the Above:

The option 'D' is incorrect as well because, as mentioned earlier, the number of polynomial zeros is equal to the number of points where the graph intersects the x-axis. So, there are points on the graph that represent the zeros of the polynomial.

In conclusion, the correct answer is option 'B' - "Intersects x-axis" because the number of polynomial zeros is equal to the number of points where the graph of the polynomial intersects the x-axis.
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A polynomials zeros can be represented graphically. The number of poly...
The number of zeroes of a polynomial is equal to the number of points where the graph of polynomial intersects the x-axis.
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A polynomials zeros can be represented graphically. The number of polynomial zeros equals the number of points on the graph of the polynomiala)Intersects y-axisb)Intersects x-axisc)Intersects y-axis or x-axisd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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