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Polynomial in One variable Video Lecture | Mathematics (Maths) Class 9

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FAQs on Polynomial in One variable Video Lecture - Mathematics (Maths) Class 9

1. What is a polynomial in one variable?
Ans. A polynomial in one variable is an algebraic expression that consists of terms with only one variable raised to non-negative integer exponents. It can be written in the form: P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where x is the variable, aₙ, aₙ₋₁, ..., a₁, a₀ are coefficients, and n is a non-negative integer.
2. How can we determine the degree of a polynomial in one variable?
Ans. The degree of a polynomial in one variable is the highest power of the variable in the polynomial. To determine the degree, we look at the term with the highest exponent of the variable. For example, in the polynomial P(x) = 3x³ - 2x² + 5x + 1, the term with the highest power is 3x³, so the degree of the polynomial is 3.
3. What are the operations that can be performed on polynomials in one variable?
Ans. The following operations can be performed on polynomials in one variable: - Addition and subtraction: Two polynomials can be added or subtracted by adding or subtracting the corresponding coefficients of the like terms. - Multiplication: Two polynomials can be multiplied using the distributive property and combining like terms. - Division: Polynomial division involves dividing one polynomial by another, resulting in a quotient and possibly a remainder.
4. How can we find the roots of a polynomial in one variable?
Ans. The roots of a polynomial in one variable are the values of the variable that make the polynomial equal to zero. To find the roots, we set the polynomial equal to zero and solve for the variable. This can be done by factoring the polynomial, using the quadratic formula for quadratic polynomials, or by using numerical methods such as Newton's method.
5. Can a polynomial in one variable have multiple roots with the same value?
Ans. Yes, a polynomial in one variable can have multiple roots with the same value. If a root of a polynomial has a multiplicity greater than 1, it means that the polynomial is divisible by the factor (x - r) raised to that multiplicity, where r is the common root. The multiplicity of a root refers to the number of times it appears as a factor in the polynomial.
57 videos|399 docs|65 tests

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