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What is the Zero of a Polynomial? Video Lecture - Class 9
FAQs on What is the Zero of a Polynomial? Video Lecture - Class 9
| 1. What is the zero of a polynomial? |  |
Ans. The zero of a polynomial is a value of the variable that makes the polynomial equal to zero. In other words, it is the value(s) of the variable for which the polynomial equation holds true.
| 2. How can we find the zeros of a polynomial? | |
Ans. To find the zeros of a polynomial, we need to equate the polynomial expression to zero and solve the resulting equation. By factoring or using the quadratic formula, we can determine the values of the variable that make the polynomial equal to zero.
| 3. Can a polynomial have more than one zero? | |
Ans. Yes, a polynomial can have more than one zero. The number of zeros of a polynomial can be determined by its degree. For example, a polynomial of degree n can have at most n distinct zeros.
| 4. What is the significance of finding zeros of a polynomial? | |
Ans. Finding the zeros of a polynomial helps us understand the behavior of the polynomial function. The zeros represent the x-intercepts or roots of the function, which are points where the graph of the polynomial intersects the x-axis. These zeros provide important information about the behavior and properties of the polynomial.
| 5. Is it possible for a polynomial to have no zeros? | |
Ans. No, a non-zero polynomial of degree greater than zero always has at least one zero. This is known as the Fundamental Theorem of Algebra, which states that every non-zero polynomial equation of degree n has exactly n complex zeros, counting multiplicities. However, it is possible for a polynomial of degree zero (a constant) to have no zeros.
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