Class 10 Exam > Class 10 Videos > 03 - Relationship Between Zeroes And Coefficient of Polynomials - Class 10 - Maths
03 - Relationship Between Zeroes And Coefficient of Polynomials - Class 10 - Maths Video Lecture
FAQs on 03 - Relationship Between Zeroes And Coefficient of Polynomials - Class 10 - Maths Video Lecture
| 1. What is the relationship between the zeroes and the coefficient of a polynomial? |  |
Ans. The relationship between the zeroes and the coefficient of a polynomial is given by Vieta's formulas. For a quadratic polynomial ax^2 + bx + c, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.
| 2. How can we find the zeroes of a polynomial if its coefficients are given? | |
Ans. We can find the zeroes of a polynomial if its coefficients are given by using various methods such as factorization, the quadratic formula, or synthetic division. These methods allow us to solve the polynomial equation and determine the values of x that make the polynomial equal to zero.
| 3. Can a polynomial have more than two zeroes? | |
Ans. Yes, a polynomial can have more than two zeroes. The number of zeroes a polynomial can have is equal to its degree. For example, a cubic polynomial can have up to three zeroes, a quartic polynomial can have up to four zeroes, and so on.
| 4. Are the zeroes of a polynomial always real numbers? | |
Ans. No, the zeroes of a polynomial are not always real numbers. They can also be complex numbers. For example, the polynomial x^2 + 1 has no real zeroes, but it has two complex zeroes, namely i and -i, where i is the imaginary unit.
| 5. What is the significance of the zeroes of a polynomial? | |
Ans. The zeroes of a polynomial are significant because they provide information about the behavior of the polynomial. The zeroes indicate the values of x for which the polynomial is equal to zero, which helps in graphing the polynomial and analyzing its properties such as the number of turning points and the behavior as x approaches infinity or negative infinity.
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Nov 15, 2024 Last updated |
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