NCERT Mathematics Class 10 Exemplar Ch 2 Polynomials Exemplar Problems Part 2 (For CBSE, ICSE, IAS, NET, NRA 2023)
Glide to success with Doorsteptutor material for CBSE/Class-10 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.
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