Q 1 – The maximum number of zeroes that a polynomial of degree 4 can have is
(a) One
(b) Two
(c) Three
(d) Four
(d) Four
Q 2 – The graph of the polynomial p(x) = 3x – 2 is a straight line that intersects the x-axis at exactly one point namely
(a) (−2/3, 0)
(b) (0, −2/3)
(c) (2/3, 0)
(d) 2/3, −2/3
(c) (2/3, 0)
Q 3 – 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
(b) both negative
Q 4 – In fig. given below, the number of zeroes of the polynomial f(x) is
(a) 1
(b) 2
(c) 3
(d) None
(c) 3
Q 5 – The zeroes of the quadratic polynomial x2 + 1750x + 175000 are
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal
(a) both negative
Q 6 – The graph of the polynomial ax² + bx + c is an upward parabola if
(a) a > 0
(b) a < 0
(b) a = 0
(d) None
(a) a > 0
Q 7 – The zeroes of the quadratic polynomial x2 + px + p, p ≠ 0 are
(a) both equal
(b) both cannot be positive
(c) both unequal
(d) both cannot be negative
(b) both cannot be p
Q 8 – 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
(a) 2
Q 9 – The graph of the polynomial ax² + bx + c is a downward parabola if
(a) a > 0
(b) a < 0
(c) a = 0
(d) a = 1
(b) a < 0
Q 10 – If α and β are the zeroes of the polynomial 5×2 – 7x + 2, then sum of their reciprocals is:
(a) 14/25
(b) 7/5
(c) 2/5
(d) 7/2
(d) 7/2
Q 11 – A polynomial of degree 3 is called
(a) a linear polynomial
(b) a quadratic polynomial
(c) a cubic polynomial
(d) a biquadratic polynomial
(c) a cubic polynomial
Q 12 – If the point (5,0), (0-2) and (3,6) lie on the graph of a polynomial. Then which of the following is a zero of the polynomial?
(a) 5
(b) 6
(c) not defined
(d) –2
(a) 5
Q 13 – If α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is
(a) 0
(b) 4
(c) –4
(d) 16
(a) 0
Q 14 – The number of zeros of a cubic polynomial is
(a) 3
(b) at least 3
(c) 2
(d) at most 3
(d) at most 3
Q 15 – If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is
(a) b – a + 1
(b) b – a – 1
(c) a – b + 1
(d) a – b – 1
(a) b – a + 1
Q 16 – If α and 
are the zeroes of the polynomial ax² + bx + c, then value of c is
(a) 0
(b) a
(c) -a
(d) 1
(b) a
Q 17 – The zeroes of the quadratic polynomial x2 + kx + k, k? 0,
(a) cannot both be positive
(b) cannot both be negative
(c) are always unequal
(d) are always equal
(a) cannot both be positive
Q 18 – If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d then α + β + γ is equal
(a) –b/a
(b) b/a
(c) c/a
(d) d/a
(a) –b/a
Q 19 – If the zeroes of the quadratic polynomial Ax2 + Bx + C, C # 0 are equal, then
(a) A and B have the same sign
(b) A and C have the same sign
(c) B and C have the same sign
(d) A and C have opposite signs
(b) A and C have the same sign
Q 20 – If x = 2 and x = 3 are zeros of the quadratic polynomial x2 + ax + b, the values of a and b respectively are :
(a) 5, 6
(b) – 5, –6
(c) –5, 6
(d) 5, –6
(c) –5, 6
Q 21 – 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) –4
(b) 4
Q 22 – If a, s are the zeroes of x² – 8x + ?, such that a – s = 2, then X =
(a) 8
(b) 22
(c) 60
(d) 15
(d) 15
Q 23 – If a polynomial of degree 4 is divided by quadratic polynomial, the degree of the remainder is
(a) ≤ 1
(b) ≥ 1
(c) 2
(d) 4
(a) ≤ 1
Q 24 – Find a and b so that the polynomial 6x4 + 8x³ – 5x² + ax + b is exactly divisible by 2x² – 5.
(a) a = 20, b = – 25
(b) a = 4, b = – 5
(c) a = 20, b = 5
(d) a = – 20, b = – 25
(d) a = – 20, b = – 25
Q 25 – If a – b, a and a + b are zeroes of the polynomial fix) = 2x³ – 6x² + 5x – 7, then value of a is
(a) 1
(b) 2
(c) -5
(d) 7
(a) 1
Q 26 – If P(x) and D(r) are any two polynomials such that D(x) ? 0, there exists unique polynomial Q(x) and R(x) such that, P(x) = D(x). Q(x) + R(x) where :
(a) R(x) = 0 and deg R(x) > deg Q(x)
(b) R(x) = 0 or deg R(x) > deg D(x)
(c) deg R(x) < deg Q(x)
(d) R(x) = 0 or deg R(x) < deg D(x)
(b) R(x) = 0 or deg R(x) > deg D(x
Q 27 – Dividend is equal to
(a) divisor × quotient + remainder
(b) divisior × quotient
(c) divisior × quotient – remainder
(d) divisor × quotient × remainder
(a) divisor × quotient + remainder
Q 28 – Write a polynomial with zeros 1, – 1 and 1.
(a) x³ + x² + x + 1
(b) x³ – x² + x + 1
(c) x³ – x² – x – 1
(d) x³ – x² – x + 1
(d) x³ – x² – x + 1
Q 29 – A quadratic polynomial whose sum of the zeroes is 2 and product is 1 is given by
(a) x² – 2x + 1
(b) x² + 2x + 1
(c) x² + 2x – 1
(d) x² – 2x – 1
(a) x² – 2x + 1
Q 30 – If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:
(a) Zero of p(x)
(b) Value of p(x)
(c) Constant of p(x)
(d) None of the above
(a) Zero of p (x)