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RD Chapter 2 Polynomials Ex VSAQS Solutions

Question - 1 : - Define a polynomial with real co-efficients.

Answer - 1 : -


Question - 2 : - Define degree of a polynomial.

Answer - 2 : - The exponent of the highest degree term in a polynomial is known as its degree. A polynomial of degree O is called a constant polynomial.

Question - 3 : - Write the standard form of a linear polynomial with real co-efficients.

Answer - 3 : - ax + b is the standard form of a linear polynomial with real co-efficients and a ≠ 0

Question - 4 : - Write the standard form of a quadratic polynomial with real co-efficients.

Answer - 4 : -

ax2 + bx + c is astandard form of quadratic polynomial with real co-efficients and a ≠ 0.

Question - 5 : - Write the standard form of a cubic polynomial with real co-efficients.

Answer - 5 : -

ax3 + bx2 + cx + d is a standard form of cubicpolynomial with real co-efficients and a ≠ 0.

Question - 6 : - Define value of a polynomial at a point.

Answer - 6 : - If f(x) is a polynomial and a is any real number then the real number obtained by replacing x by α in f(x) is called the value of f(x) at x = α and is denoted by f(α).

Question - 7 : - Define zero of a polynomial.

Answer - 7 : - A real number a is a zero of a polynomial f(x) if f(α) = 0.

Question - 8 : - The sum and product of the zeros of a quadratic polynomial are – 1/2 and -3 respectively. What is the quadratic polynomial ?

Answer - 8 : -


Question - 9 : - Write the family of quadratic polynomials having – 1/4 and 1 as its zeros.

Answer - 9 : -


Question - 10 : - If the product of zeros of the quadratic polynomial f(x) = x2 – 4x + k is 3, find the value of k.

Answer - 10 : -

We know that a quadratic polynomial x2 –(sum of zeros) x + product of zeros
In the given polynomial f(x) = x2 –4x + k is the product of zeros which is equal to 3
k = 3

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