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Q1. If -2 is a zero of p(x) = (ax³ + bx² + x – 6) and p(x) leaves a remainder 4 when divided by (x – 2), then the values of a and b are (respectively):
(a) a = 2,b = 2
(b) a = 0,b = – 2
(c) a = 0, b = 2
(d) a = 0, b = 0
(c) a = 0, b = 2 If – 2 is a zero => p(- 2) = 0 => – 2a + b = 2 Also, p(2) = 4 2a + b = 2=>a = 0and b = 2
Q2. If x101 + 1001 is divided by x + 1, then remainder is:
(a) 0
(b) 1
(c) 1490
(d) 1000
(d) 1000 p(x) is divided by x + 1 p(- 1) = (-1101) + 1001 = 1000
Q3. If one zero of a polynomial p(x) = ax² + bx + c(a ? 0) is zero, then, which of the following is correct:
(a) b = 0
(b) c = 0
(c) other zero is also zero
(d) Nothing can be said about p(x).
(b) c = 0
Q4. sum of the squares of the zeroes of the polynomial p(x) = x² + 7x – k is 25, find k.
(a) 12
(b) 49
(c) – 24
(d) – 12
(d) – 12
Q5. Let, a, s, v be the zeroes of x³ + 4x² + x- 6 such that product of two of the zeroes is 6. Find the third zero.
(a) 6
(b) 2
(c) 4
(d) 1
(a) 6
Q6. 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
Q7. 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
Q8. If the zeros of the polynomial x³ – 3x² + x +1 are p – q,p and p + q. Find the value of q.
(a) 1
(b) 0
(c) 2
(d) ±v2
(d) ±v2
Q9. A quadratic polynomial has :
(a) at least 2 zeros
(b) exactly 2 zeros
(c) at most 2 zeros
(d) exactly 1 zero
(c) at most 2 zeros A quadratic polynomial has atmost two zeroes.
Q10. 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) division algorithm
Q11. When we divide x³ + 5x + 7 by x4 – 7x² – 6 then quotient and remainder are (respectively):
(a) 0,x³ + 5x + 7
(b) x, 2x + 3
(c) 1,x4 – 7x²-6
(d) x², 4x – 9
(a) 0,x³ + 5x + 7
Q12. The value of b, for which 2x³ + 9x² – x – b is exactly divisible by 2x + 3 is:
(a) -15
(b) 15
(c) 9
(d) – 9
(b) 15
Q13. If a and s are two zeros of the polynomial p(x), then which of the following is a factor of p(x):
(a) (x – a)(x – s)
(b) (x + a) (x + s)
(c) k(x – a)
(d) k(x- s)
(a) (x – a)(x – s)
Q14. Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and the product of its zeros as -2, +5, -3, respectively.
(a) 2x³ + 5x² + x + 3
(b) 4x³ + 5x² – 3x + 7
(c) x³ + 2x² + 5x + 3
(d) 2x³ + 5x² + 3x + 1
(c)
Q15. 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
Q16. If 2 is a zero of p(x) = x² + 3x + k, find k:
(a) 10
(b) 5
(c) – 3
(d) – 10
(d) – 10
Q17. The number of polynomials having zeroes – 1 and – 5 is :
(a) 2
(b) 3
(c) 1
(d) More than 3
(d) More than 3
Q18. The number of polynomials having zeroes as 4 and 7 is
(a) 2
(b) 3
(c) 4
(d) more than 4
(d) more than 4
Q19. 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
Q20. 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
Q21. Find the quadratic polynomial whose zeros are 2 and -6
(a) x2 + 4x + 12
(b) x2 – 4x – 12
(c) x2 + 4x – 12
(d) x2 – 4x + 12
(c) x2 + 4x – 12
Q22. 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
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