CBSE Class 10 Mathematics Polynomials MCQs Set 03

Question: If a and 1/α are the zeroes of polynomial 4x² -2x +(k- 4), the value of k is:
a) 4
b) 8
c) 0
d) None of the options
Answer: b

Question: Which of the following is a polynomial: C
a) x² + 1/x
b) 2x² -3√x +1
c) 3x² -3x +1
d) x² + x ^-2 +7
Answer: c

Question: If a polynomial of degree 6 is divided by a polynomial of degree 2, then the degree of the quotient is
a) less than 4
b) less than 2
c) equal to 2
d) equal to 4
Answer: d

Question: If f(x) = ax² + bx + c has no real zeroes and a + b + c < 0, then:
a) c = 0
b) c > 0
c) c < 0
d) None of the options
Answer: c

Question: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the 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 negative.
d) can have a linear term but the constant term is positive.
Answer: a

Question: The quadratic polynomial having zeroes –3 and 2 is
a) x² - x -6
b) x² + x -6
c) x² + x +6
d) x² - x +6
Answer: b

Question: If the sum of the zeroes of the polynomial f(x) = 2x³ -3kx² + 4x -5 is 6, then the value of k is:
a) 2
b) 4
c) –2
d) –2
Answer: b

Question: If 5 is a zero of the quadratic polynomial x² - kx -15, then the value of k is
a) 2
b) –2
c) 4
d) – 4
Answer: a

Question: If a, b are the zeroes of the polynomial f(x) = x² -3x +2, then 1/α 1/β + equals to:
a) 3
b) –1
c) 3/2
d) - 3/2
Answer: c

Question: If α,β,y are the zeroes of the polynomial p(x) = x³ - ax² + bx - c then 1/αβ + 1/αβ + 1/αβ = __________
a) a/b
b) b/c
c) a/c
d) c/d
Answer: c

Question: If p and q are the zeroes of the quadratic polynomial f(x) = ax² + ax + b then the value of p⁴ + q⁴ is ______
a) (a² - 2bc)² - b²c²/c⁴
b) (a² - 2bc)² - 2b²c²/c⁴
c) (b² - 2ac)² - a²c²/c⁴
d) (b² - 2ac)² - 2a²c²/c⁴
Answer: b

Question: If √(5/3) and -√(5/3) are two zeroes of the polynomial 3x⁴ +6x³ -2x² -10x -5, then its other two zeroes are:
a) –1, –1
b) 1, –1
c) 1, 1
d) 3, –3
Answer: a

Question: If one of the zeroes of the quadratic polynomial (k -1) x² + kx +1 is –3, then the value of k is
a) 4/3
b) -4/3
c) 2/3
d) -2/3
Answer: a

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 product and sum of zeroes of the quadratic polynomial ax² + bx + c are respectively.
a) b/a , c/a 
b) c/a , b/a
c) c/b , 1
d) c/a , -b/a
Answer: d

Question: If the polynomial f(x) = ax³ + bx - c is divisible by the polynomial g(x) = x² + bx + c, then the value of ab
is:
a) 1/c
b) 1
c) –1
d) None of the options
Answer: b

Question: If one zero of the quadratic polynomial x² -5x + k is –4 ,then the value of k is
a) 36
b) –36
c) 18
d) –18
Answer: b

Question: If a,b are the zeroes of the polynomial f(x) = ax² + bx + c, then 1/α² 1/β² + equals to:
a) b²-4ac/a² 
b) b²-2ac/c² 
c) b²-2ac/a² 
d) b²+2ac/c²
Answer: b

Question: Given that two of the zeroes of the cubic polynomial ax³ + bx² + cx + d are 0, the value of c is
a) less than 0
b) greater than 0
c) equal to 0
d) can’t say
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: If the zeroes of the quadratic polynomial ax² + bx + c, c ¹ 0 are equal, then
a) c and a have opposite signs
b) c and a have the same sign
c) c and b have opposite signs
d) c and b have the same sign
Answer: b

Question: If the product of two zeroes of the polynomial p(x) = 2x³ +6x² - 4x +9 is 3, then its third zero is
a) -3/2
b) 3/2
c) -9/2
d) 9/2
Answer: a

Question: If the zeroes of the quadratic polynomial ax²+ bx + c, c≠0 are equal, then
a) c and a have opposite signs
b) c and b have opposite signs
c) c and a have the same sign
d) c and b have the same sign
Answer: c

Question: Given that two of the zeroes of the cubic polynomial ax³ + bx 2 + cx + d are 0, the value of c is
a) less than 0
b) greater than 0
c) equal to 0
d) can’t say
Answer: c

Question:If the zeroes of the polynomial f(x) = ax³ + 3bx² 3cx + d are in A.P. then 2b³ + a²d is equal to _______
a) a² bc
b) 3abc
c) 2b² ac
d) abc
Answer: b

Question: If the zeroes of the quadratic polynomial ax² + bx + c, c ¹ 0 are equal, then
a) c and a have opposite signs
b) c and a have the same sign
c) c and b have opposite signs
d) c and b have the same sign
Answer: b

Question: A quadratic polynomial with 3 and 2 as the sum and product of its zeroes respectively is
a) x² +3x -2
b) x² -3x +2
c) x² -2x +3
d) x² -2x -3
Answer: b

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: A quadratic polynomial with sum and product of its zeroes as 8 and –9 respectively is
a) x² -8x +9
b) x² -8x -9
c) x² +8x -9
d) x² +8x +9
Answer: b

Question: If the graph of a polynomial intersects the x-axis at exactly two points, then it
a) cannot be a linear or a cubic polynomial
b) can be a quadratic polynomial only
c) can be a cubic or a quadratic polynomial
d) can be a linear or a quadratic polynomial
Answer: d

Question: A quadratic polynomial whose roots are –3 and 4 is
a) x² - x +12
b) x² + x +12
c) x²/2 - x/2-6
d) 2x² +2x -24
Answer: c

Question: If one of the zeroes of the cubic polynomial x ³ + ax² + bx + c is –1, then the product of the other two zeroes is
a) a - b -1
b) b - a -1
c) b - a +1
d) a - b +1
Answer: a

Question: If the LCM of p(x) and q(x) is a⁹ b⁹ then their HCF can be
a) (a - b)
b) (a² + b² + ab)
c) a⁶ + b⁶ + a³b³
d) all of the options
Answer: d

Question: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the 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 negative.
d) can have a linear term but the constant term is positive.
Answer: a

Question: If p(x) = ax²+ bx + c has no real zero and a + b + c < 0, then
a) c = 0
b) c < 0
c) c > 0
d) None of the options
Answer: b

 Question: If one root of the polynomial p(y) = 5y² +13y + m is reciprocal of other, then the value of m is
a) 6
b) 0
c) 5
d) 1/5
Answer: c

Question: If two zeroes of the polynomial f (x) = x⁴ - 2x³ - 18x² - 6x + 45 are , -√3 and √3 then find the sum of other two zeroes.
a) 0
b) -1
c) -2
d) 1
Answer: c

Question: if p(x) = x² + x + 1 and q (x) = x³ - x + 1, then the HCF of p b) and q a)
a) c + b + 1
b) a - b + 1
c) a - b
d) a + b
Answer: c

Question: The zeroes of the quadratic polynomial x² + ax + b a, b > 0 are
a) both positive
b) both negative
c) one positive one negative
d) can’t say
Answer: b

Question: The degree of the remainder r(x) when p(x)= bx³ + cx + d is divided by a polynomial of degree 4 is
a) less than 4
b) less than 3
c) equal to 3
d) less than or equal to 3
Answer: c