Class 9 Exam > Class 9 Videos > Advance Learner Course: Mathematics (Maths) Class 9 > Relationship between Zeroes & Coefficient of Polynomials
Relationship between Zeroes & Coefficient of Polynomials Video Lecture | Advance Learner Course: Mathematics (Maths) Class 9
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FAQs on Relationship between Zeroes & Coefficient of Polynomials Video Lecture - Advance Learner Course: Mathematics (Maths) Class 9
| 1. What is the relationship between zeroes and the coefficient of polynomials? |  |
Ans. The relationship between the zeroes and the coefficient of polynomials is given by Vieta's formulas. For a polynomial of degree n, the sum of its zeroes is equal to the ratio of the coefficient of the second highest degree term to the coefficient of the highest degree term, multiplied by (-1) raised to the power of n. The product of the zeroes is equal to the ratio of the constant term to the coefficient of the highest degree term, multiplied by (-1) raised to the power of n.
| 2. How can the coefficient of a polynomial be determined from its zeroes? | |
Ans. To determine the coefficient of a polynomial from its zeroes, we can use Vieta's formulas. For a polynomial of degree n, the coefficient of the second highest degree term is equal to the sum of the product of the zeroes taken two at a time, multiplied by (-1). The constant term is equal to the product of all the zeroes, multiplied by (-1) raised to the power of n.
| 3. Can a polynomial have zeroes with different coefficients? | |
Ans. No, a polynomial cannot have zeroes with different coefficients. The zeroes of a polynomial are the values of the variable for which the polynomial equation becomes zero. Since the coefficient of each term in the polynomial determines its contribution to the value of the polynomial, the zeroes must satisfy the equation formed by equating the polynomial to zero. Therefore, all the zeroes of a polynomial have the same coefficient.
| 4. How can the coefficient of a polynomial affect its zeroes? | |
Ans. The coefficient of a polynomial can affect its zeroes in several ways. If a polynomial has a zero of multiplicity greater than 1, it means that the corresponding factor of the polynomial is repeated. This repetition is influenced by the coefficient of the polynomial. Additionally, the coefficient of the highest degree term in a polynomial can determine the overall behavior of the polynomial, such as whether it has a positive or negative leading coefficient, which in turn can affect the number and nature of its zeroes.
| 5. Can the coefficient of a polynomial be zero? | |
Ans. Yes, the coefficient of a polynomial can be zero. In a polynomial expression, each term consists of a coefficient multiplied by the variable raised to a certain power. If the coefficient of a term is zero, it means that the variable is absent from that term. This can happen when certain powers of the variable are missing from the polynomial expression. However, it's important to note that a polynomial is defined by having non-zero coefficients for at least one term.
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