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If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial is ______
- a)Linear
- b)Quadratic
- c)Cubic
- d)Biquadratic
Correct answer is option 'C'. Can you explain this answer?
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If the graph of a polynomial cuts the x-axis at 3 points, then the pol...
Since, the graph of the polynomial cuts the x-axis at 3 points, hence, it will be a cubic polynomial. A polynomial is said to be linear, quadratic, cubic or biquadratic according to the degree of the polynomial.
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If the graph of a polynomial cuts the x-axis at 3 points, then the pol...
Explanation:
Polynomial Degree:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- For example, in the polynomial x^2 + 2x + 1, the degree is 2.
Number of x-intercepts:
- The number of times a graph cuts the x-axis represents the number of real roots of the polynomial.
- Each x-intercept corresponds to a real root of the polynomial.
Cubic Polynomial:
- A cubic polynomial is of the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.
- A cubic polynomial has a degree of 3 and can have up to 3 real roots.
- The graph of a cubic polynomial can cut the x-axis at a maximum of 3 points.
Conclusion:
- If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial must be a cubic polynomial.
- Therefore, the correct answer is option 'C) Cubic'.
Polynomial Degree:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- For example, in the polynomial x^2 + 2x + 1, the degree is 2.
Number of x-intercepts:
- The number of times a graph cuts the x-axis represents the number of real roots of the polynomial.
- Each x-intercept corresponds to a real root of the polynomial.
Cubic Polynomial:
- A cubic polynomial is of the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.
- A cubic polynomial has a degree of 3 and can have up to 3 real roots.
- The graph of a cubic polynomial can cut the x-axis at a maximum of 3 points.
Conclusion:
- If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial must be a cubic polynomial.
- Therefore, the correct answer is option 'C) Cubic'.
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