NCERT Mathematics Class 10 Exemplar Ch 2 Polynomials Exemplar Problems Part 2

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EXERCISE 2.2

(i) Can be the quotient on division of by a polynomial in x of degree 5?

Answer: No

(ii) What will the quotient and remainder be on division of by , ?

Answer:

(iii) If on division of a polynomial by a polynomial , the quotient is zero, what is the relation between the degrees of and ?

Answer:

(iv) If on division of a non-zero polynomial by a polynomial , the remainder is zero, what is the relation between the degrees of and ?

Answer:

(v) Can the quadratic polynomial has equal zeroes for some odd integer ?

Answer: No

(i) If the zeroes of a quadratic polynomial are both positive, then a, b and c all have the same sign.

Answer: False

(ii) If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

Answer: False

(iii) If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

Answer: True

(iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Answer: True

(v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

Answer: True

(vi) If all three zeroes of a cubic polynomial are positive, then at least one of a, b and c is non-negative.

Answer: False

(vii) The only value of k for which the quadratic polynomial has equal zeros is

Answer: False