### Common Errors in Secondary Mathematics

Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

### Math Assignment Ch-2 Class X | Polynomials

Mathematics Assignment
Important and useful questions on quadratic polynomial, Extra questions based on quadratic polynomial class 10 for the examination point of view. A complete and useful assignment on quadratic polynomial.

## ASSIGNMENT | CHAPTER-2

POLYNOMIALS

Q1- Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

(a) 4x² - 4x + 1   [Ans; 1/2],

(b)  x² - 2x - 6     [Ans; 3, -],

(c)  x² - 8x + 12   [Ans; 6, 2]

(d) 2x² + 5x + 2    [Ans  -2, -1/2]

(g)   x² - 8           [Ans; ± 2],

(h) 9y² - 6y + 1    [Ans; 1/3, 1/3],

(i)  3x² - 5x - 2      [Ans; 2, -1/3]

Q2- Find sum and product of zeroes of

(a) 2x² + 2x + 3        [Ans; -1, 3/2],

(b) x² - 7x - 7            [Ans; 7, -7]

c)

Q3- Find a quadratic polynomial whose sum and product of zeros are

(a)           [Ans; 6x² - 2x + 3]

(b)

(c)       [ Ans; x² +  x +  ]

(d)

(e)

Q4- If x + a is the factor of 2x2 + 2ax + 5x + 10, then find a

[Ans a = 2]

Q5) For what value of k,  -4 is a zero of the polynomial  x2 – x - (2k + 2) ?

[Ans k = 9]

Q6) - Find a if 2x - 3 is a factor of 6x³ - x² - 10x + a.

[Ans; a = - 3]

Q7)  For what value of k is -3 a zero of x² + 11x + k.

Q8)  If 1 is the zero of ax² - 3(a - 1)x - 1 then find a.

Ans; a = 1

Q9)  Is (x + 2) a factor of 2x² + 3x + 1.

Q 10)  If α, β are the zeroes of P(x) = ax² + bx + c then find

a)

b)

c)

d)

e)

Q11- If the zeroes of x2 – Kx + 6 are in the ratio 3 : 2, find K

Q12. What is the degree of the polynomial (x + 1)(x2 – x - x4 + 1)

Q13 If α, β are the roots of P(x) = x² - 6x + k then what is the value of k if 3α + 2β = 20.

[Ans; k = - 16]

Q14 If α, β are the zeroes of P(y) = 2y² + 7y + 5 then find α + β +  αβ.

Q15. A polynomial P(x) is divisible by  (x - 4) and 2 is the zero of P(x), then write the corresponding polynomial.

Q16)  If α, β are the zeroes of P(x) = x- 5x + 4, then find the value of

a)           [Ans: 5/4]

b)        [Ans:  320]

Q17)  If α, β  are the zeroes of P(x) = x2 - 1, then find a quadratic polynomial whose zeroes are

Ans[x2 + 4x + 4]

Q18.  If α, β are the zeros of the polynomial 25p2 – 15p + 2, then find a quadratic polynomial whose zeroes are

Q19) If α, β are the zeroes of  4x2 + 4x + 1, then form a quadratic polynomial whose zeroes are  2α, 2β

Q 20) For what value of p, - 4 is the zero of P(x) = x- 2x - (7p + 3)
Q 21) If one zero of  (a2 + 9) x2 + 13x + 6a  is the reciprocal of the other then find the value of a

Q22) If sum of zeroes of ky2 + 2y – 3k  is equal to the twice their product , find the value of k

Q 23) If  α, β  are the zeroes of  P(x) = x2 – x – k  such that α – β  = 9, find the value of k.

Q 24)  If p and q are the zeroes of 2x2 – 7x + 3 then find the value of p2 + q2

Q 25) A quadratic polynomial 2x2 - 3x + 1 has zeroes as α and β  . Now form the quadratic polynomial whose zeroes are  3α and  3β

Q 26) If α, β are the zeroes of  x2 + 4x + 3, find the polynomial whose zeroes are    and

Q 27)  Find a quadratic polynomial whose zeroes are

QUESTIONS DELETED FROM CBSE SYLLABUS

Q28) Find k so that x2 + 2x + k is a factor of  2x4 + x3 – 14x2 + 5x + 6

Ans[k = - 3, - 1]

Q29- Find quotient and remainder on dividing P(x) by g(x)

(a)  P(x) = x⁴ + x² + 1; g(x) = x² + x + 1

Ans; q(x) = x² - x + 1

(b)    P(y) = 4y⁴ - 10y³ - 10y² + 30y - 15; g(y) = 2y - 5

Ans; q(y) = 2x3 - 5x + 5/2

(c)   P(x) = 2x⁴ + 8x³ + 7x² + 4x + 5; g(x) = x + 3

Ans; q(x) = 2x³ + 2x² + x + 1

Q30)  Find a and b so that x⁴ + x³ + 8x² + ax - b is divisible by x² + 1.

[Ans; a = 1, b= - 7]

Q31- Verify that 1, 1/2, -2 are the zeroes of P(x) = 2x³ + x² - 5x + 2.

Q32- Find all zeroes of 2x³ + x² - 6x - 3 if its 2 zeroes are  ±

Q33- Find all the zeroes of  2x³ + x² - 5x + 2 if one of zero is 1/2.

Ans; 1, - 2

Q34- If -1 is one of the zero of P(x) = 3x³ - 5x² - 11x - 3. Find other zeroes and verify the relation between  zeroes and coefficients.

[Ans; All zeroes are  -1,  3, -1/3]

Q35) Obtain all zeroes of f(x) = x+ 13x+ 32x + 20, if one zero is -2

[Ans: All zeroes are  -10,  -1,  - 2]

Q36)  Find all the zeroes of 3x⁴ + 6x³ - 2x² - 10x - 5 if its two zeroes are

[Ans:  - 1, - 1]

Q37) Find all zeroes of 2x⁴ - 3x³ - 3x² + 6x - 2 if its two zeroes are

[Ans: 1]

Q38) Obtain all zeroes of f(x) = 2x- 2x- 7x+ 3x + 6, if its two zeroes are
[Ans:  2, -1]

Q39) Obtain all zeroes of p(x) =  2x4 + x3 – 14x2 – 19x – 6, if two of zeroes are -2 and -1

[Ans: -1/2, 3,  -2, -1]

Q40) Find all zeroes of P(x) = x⁴ + x³ - 23x² - 3x + 60 if its 2 zeroes are

Q41)  Find all zeroes of P(x) = x⁴ + x³ - 34x² - 4x + 120 if its two zeroes are  ± 2,

[Ans; 5, - 6]

Q42)  P(x) = x⁴ - 5x + 6,   g(x) = 2 - x² find q(x) and r(x) if P(x) is divided by g(x).

[Ans: q(x) = - x² - 1,  r(x) = - 5x + 10]

Q43- On dividing 10x⁴ - 6x³ - 40x² + 41x - 5 by g(x) the quotient is 5x - 3 and remainder is 2x + 4, Find g(x).

[Ans: 2x³ - 8x + 3]

Q44- If one zero of the P(x) = 5x² + 13x + k is the reciprocal of the other then the value of k is?

[Ans; 5]

Q45- What must be subtracted from 8x⁴ + 14x³ - 2x² + 7x - 8 so that the resulting polynomial is divisible by  4x² + 3x - 2.

[Ans; 14x - 10]

Q46) What must be subtracted from z⁵ - 9z + 6 so that it is exactly divisible by z² + 3.

[ Ans; 6]

Q47)  What must be added to the polynomial p(x) = x+ 2x- 13x- 12x + 21 so that the resulting polynomial is exactly divisible by x- 4x + 3

[Ans:   - 2x + 3]

Q48- What must be added to x⁴ + 2x³ - 2x² - x - 2 so that the resulting polynomial is  divisible by  x² + 2x - 3.

[Ans; 3x - 1]

Q49) If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial  3x2 + 4x + 1, the remainder comes out to be  ax + b, find a and b

Ans [a = 1 & b = 2]

Q50) Using division algorithm show that 6y5 + 15y4 + 16y3 + 4y2 + 10y – 35  is divisible by  3y2 + 5

Q51) On dividing the polynomial 9x4 – 4x2 + 5 by 3x2 + x - 1   remainder is ax - b. Find a and b

Q 52) Polynomial x4 + 7x3 + 7x2 + px + q  is exactly divisible by x2 + 7x + 12, then find the value of p and q .

Q 53) If x -    is the factor of x- 3  x2 - 5x + 15  then find all zeroes of this polynomial.

Q 54) If x3 + 8x2 + kx + 18 is divisible by x2 + 6x + 9 then find the value of k.

Q 55) If 3x4 – 9x3 + x2 + 15x + k is divisible by 3x2 - 5 , find the value of k and other two zeroes  of the polynomial .

Q 56) On dividing x- 8x+ 20x - 10 by g(x)  the quotient and remainder were x - 4 and 6 respectively . Find g(x)

Q 57) Find all zeroes of x- 17x- 36x - 20, if two of its zeroes are  5 and  -2

Q 58)  Find all zeroes of  x4 – 3  x3 + 3x2 + 3  x - 4 if two of its zeroes are  and 2

Q 59) What must be added or subtracted to 8x+ 14x- 2x+ 8x - 12 so that 4x+ 3x - 2 is a factor of p(x).

Q 60) If x+ 2x+ 8x+ 12x + 18 is divided by another polynomial x+ 5, the remainder is px + q . Find the value of p and q .

## 🙏

1. Thankuuuuuuuuuu