Assignment
Grade: X
Subject: Mathematics
Chapter: 02
Topic: Polynomials
1 Mark Questions
Q1. Form a quadratic equation whose zeroes are 11 and 2.
Q2. Write a quadratic polynomial, whose zeroes are 5 and –6.
Q3. Find a quadratic polynomial whose zeroes are 5 + √ 2 and 5 – √ 2 .
Q4. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively.
Q5. If one zero of the polynomial x 2−4 x+1 is 2 + √ 3, find the other zero.
Q6. If one zero of 3x2 – 4x + p is reciprocal to the other, then find the value of p.
Q7. For what value of k ,(−4) is a zero of the polynomial x 2−x−(2 k +2) ?
2 Marks Questions
Q8. Find the zeroes of √ 3 x2 +10 x+ 7 √ 3 .
Q9. If one zero of the quadratic polynomial x2 + 3x + k is 2, then find the value of k.
Q10. If the sum of the zeroes of polynomial k y 2 +2 y−3 k is equal to twice their product, find the value of
k.
Q11. If a and b are the zeroes of the polynomial x2 – 11x + 30, Find the value of a3 + b3.
Q12. If 2 is the zero of polynomial px2 + (p – 2)x + 2, what is the value of p?
Q13. If the polynomial 6 x 4 +8 x 3 +17 x 2+21 x+ 7 is divided by another polynomial 3 x 2+ 4 x +1, the remainder
is (ax +b). Find the value of a∧b .
Q14. If in division algorithm dividend = x3 ⎼ 6x2 + 7x + 5, divisor = x ⎼ 2 and remainder = 3, then find the
quotient.
Q15. If in division algorithm dividend = x4 ⎼ 8x3 + 7x + 5, divisor = x + 5, find the quotient and remainder.
1 1
Q16. Find the value of and , if p and q are the zeroes of polynomial x2 + ax + b.
p q
3 Marks Questions
Q17. Find the zeroes of 2x3 – 11x2 + 17x – 6.
Q18. Find all the zeroes of the polynomial x 3+ 13 x 2 +32 x+20 , if one of the zeroes is −2.
Q19. For what value of k, –7 is the zero of the polynomial 2x2 + 11x + (6k – 3)? Also find the other zero of
the polynomial?
Q20. If the polynomial f(x) = x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the
remainder comes out to be x + a, find k and a.
Q21. When a polynomial x4 + 2x3 + 8x2 + 12x + 18 is divided by another polynomial x2 + 5. If the remainder
comes out to be ax ⎼ b, find the values of a and b.
Q22. Find the values of a∧b so that x 4 + x 3 +8 x 2+ ax−b is divisible by x 2+ 1.
Q23. If ∝∧β are zeroes of the polynomial 4 x2 + 4 x+ 1, then form a polynomial whose zeroes are ∝2∧β 2.
Q24. If ∝∧β are zeroes of the polynomial 4 x2 + 4 x+ 1, then form a polynomial whose zeroes are 2 ∝∧2 β .
Q25. If α and β are the zeroes of the quadratic polynomial f(x) = 2x2 – 5x + 7, find a polynomial whose
zeroes are 2α + 3β and 3α + 2β.
Q26. If α and β are the zeroes of the quadratic polynomial f(x) = 3x2 + 4x + 5, find the value of α4 + β4.
Q27. If α and ß are the zeroes of the polynomial f ( x )=x 2−1 , find a quadratic polynomial whose zeroes are
2α 2ß
and .
ß α
4 Marks Questions
Q28. Divide 2 x 4−9 x 3 +5 x2 +3 x−8 by x 2−4 x+1 and verify the division algorithm.
Q29. Using division algorithm check whether 2y – 5 is a factor of 4y4 – 10y3 – 10y2 + 30y – 15.
Q30. Check whether g(x) = x2 – 3 is a factor of p(x) = 2x4 + 3x3 – 2x2 – 9x – 12 by applying division
algorithm.
Q31. On dividing f ( x )=3 x 3−2 x 2+5 x−5 by polynomial p(x ), the quotient and remainder are x 2−x +2 and
−7 respectively. Find p(x ).
Q32.Find all the zeroes of the polynomial x4 – 3x3 + 6x – 4, if two of its zeroes are √ 2 and −√ 2.
Q33. Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two
polynomials.
Q34. If one zero of the polynomial f ( x )=4 x 2−8 kx +8 x−9 is negative of the other, then find the zeroes of
2
k x + 3 kx +2.
Q35.Find k so that the polynomial x2 + 2x + k is a factor of polynomial 2x4 + x3 – 14x2 + 5x + 6. Also, find
all the zeroes of the two polynomials.
Q36. If α and β are the zeroes of the quadratic polynomial f(x) = x2 – p (x + 1) – c, show that (α + 1) (β + 1)
= 1 – c.
