CBSE Class 10 Mathematics Polynomials MCQs Set D

Question: The zeroes of 3x ² +10x +7 3 are:
a) 7, 3
b) √3,7 √3
c) -√ 3 -7/√3,
d) None of the options
Answer: c

 Question: If a and b are zeroes of p(x) = x² + x -1, then 1/α + 1/β + equals to
a) –1
b) 1
c) 2
d) 0
Answer: b

Question: The zeroes of the quadratic polynomial x² +99x +127 are
a) both positive
b) both negative
c) one positive and one negative
d) both equal
Answer: b

Question: If the zeroes of the algebraic expression 3ax² + x(3b + 5a are -3/7 and -5/3 , then find the value of a/b
a) 1/3
b) 4/5
c) 7/3
d) 3
Answer: b

Question: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is negative of the other, then it 
a) has no linear term and the constant term is negative
b) has no linear term and the constant term is positive
c) can have a linear term but the constant term is positive
d) can have a linear term but the constant term is negative
Answer: a

Question: If the zeroes of the quadratic polynomial x² +(a +1)x + b are 2 and –3, then
a) a = -7, b = -1
b) a = 5, b = -1
c) a = 2, b = -6
d) a = 0, b = -6
Answer: d

Question: If f(x) = 3x⁴ + 6x³ - 2x^{2 -} l0x - 5 and two of its zeroes are - 1, - 1, then the other two zeroes are _______
a) √3/5 - √3/5
b) √2/5 - √2/5
c) √5/3 - √5/3
d) √5/4 - √5/4
Answer: c

Question: Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is
a) -c/a
b) c/a
c) 0
d) -b/a
Answer: b

Question: The zeroes of the quadratic polynomial x² + kx + k, k ≠ 0
a) cannot both be positive
b) cannot both be negative
c) are always equal
d) are always unequal
Answer: a

Question: The number of polynomials having exactly two zeroes 1 and –2 is
a) 1
b) 2
c) 3
d) infinitely many
Answer: a

Question: A quadratic polynomial, whose zeroes are 5 and –8 is
a) x² +13x - 40
b) x² + 4x -3
c) x² -3x + 40
d) x² +3x - 40
Answer: d

Question: Solve

Answer: d

Question: The graph of a polynomial f(x) is shown below

The number of real zeroes of the polynomial f(x) is _________
a) 1
b) 2
c) 3
d) 4
Answer: d

Question: Can x 2 -1 be the quotient on division of x 6 +2x 3 + x -1 by a polynomial in x of degree 5?
Answer: No 

Question: Can (x -2) be the remainder of a polynomial when divided by p(x) = 3x + 4? Justify.
Answer: No

Question: If two of the zeroes of a cubic polynomial are zero, then does it have linear and constant terms? Give reason. 
Answer: No

Question: If the graph of a polynomial intersects the x-axis at only one point can it be a quadratic polynomial?
Answer: Yes

Question: If all the zeroes of cubic polynomial are negative, what can you say about the signs of all the coefficient and the constant term? Give reason.
Answer: Same sign

Question: If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?
Answer: deg g(x) £ deg p(x)

Question: What will be the degree of quotient and remainder on division of x 3 +3x -5 by x 2 +1? Justify.
Answer: Degree of Quotient = 1, Degree of Remainder = 1

Question: If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?
Answer: deg g(x) £ deg p(x)

Question: If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?
Answer: deg p(x) < deg g(x)

Question: The degree of a cubic polynomial is at least 3. State true or false. Give reason. 
Answer: F, because it is equal to 3.

Question: A linear polynomial can have atmost one zero. State true or false.
Answer: T

Question: The only value of k for which the quadratic polynomial kx 2 + x + k has equal zeroes is 1/2.
Answer: False

Question: A quadratic polynomial has at least one zero. State true or false. 
Answer: F

Question: If all the zeroes of a cubic polynomial are negative, then all the coefficients and constant term of the polynomial have the same sign.
Answer: True

Question: If the graph of a polynomial intersects the x-axis exactly at two points, it may not be quadratic polynomial. State true or false. Give reason.
Answer: T

Question: The only value of k for which the quadratic polynomial kx 2 + x + k has equal zeroes is 1/2 , state true or false.
Answer: F

Question: If all three zeroes of a cubic polynomial x 3 + ax 2 - bx + c are positive, then at least one of a, b and c is non-negative.
Answer: False

Question: If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Answer: True