### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

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

Mathematics Assignment
Class 10, Chapter 2, Quadratic Polynomials
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.

## LEVEL - 1

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 - 2$\sqrt{2}$x - 6     [Ans; 3$\sqrt{2}$, -$\sqrt{2}$],

(c)  x² - 8x + 12   [Ans; 6, 2]

(d) 2x² + 5x + 2    [Ans  -2, -1/2]

$e)\: \: \sqrt{3}x^{2}-8x+4\sqrt{3}\: \: \: \left [ Ans:\: \frac{2}{\sqrt{3}},\: 2\sqrt{3} \right ]$

$f)\: \: 4\sqrt{3}x^{2}+4\sqrt{3}x-3\sqrt{3}\: \: \: \left [ Ans:\: \frac{-3}{2},\: \frac{1}{2} \right ]$

(g)   x² - 8           [Ans; ± 2$\sqrt{2}$],

(h) 9y² - 6y + 1    [Ans; 1/3, 1/3],

(i)  3x² - 5x - 2      [Ans; 2, -1/3]

$j)\: \: 6x^{2}+17x+12\: \: \: \left [ Ans:\: \frac{-4}{3},\: \frac{-3}{2} \right ]$

$k)\: \: 24x^{2}-41x+12\: \: \: \left [ Ans:\: \frac{4}{3},\: \frac{3}{8} \right ]$
$l)\: \: 15x^{2}-x-28\: \: \: \left [ Ans:\: \frac{7}{5},\: \frac{-4}{3} \right ]$
$m)\: \: 5\sqrt{5}x^{2}+20x+3\sqrt{5}\: \: \: \left [ Ans:\: \frac{-3}{\sqrt{5}},\: \frac{-\sqrt{5}}{5} \right ]$

$n)\: \: 6\sqrt{3}x^{2}-47x+5\sqrt{3}\: \: \: \left [ Ans:\: \frac{5\sqrt{3}}{2},\: \frac{1}{3\sqrt{3}} \right ]$

Q2- Find sum and product of zeroes of

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

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

c)  $4\sqrt{3}x^{2}+7x-2\sqrt{3}\: \: \: \left [ Ans:\: \frac{-7}{4\sqrt{3}},\: \frac{-1}{2} \right ]$

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

(a)    $\frac{1}{3}\: and\: \frac{1}{2}$       [Ans; 6x² - 2x + 3]

(b)  $0\: and\: \sqrt{3}\: \: \: \: \: [Ans:\: x^{2}+\sqrt{3}]$

(c)  $-\sqrt{2}\: and\: \sqrt{3}$     [ Ans; x² + $\sqrt{2}$ x + $\sqrt{3}$ ]

(d)   $0\: and\: \frac{-\sqrt{7}}{2}$       $[Ans:\: 2x^{2}-\sqrt{7}]$

(e)     $\frac{5}{7}\: and\: \frac{10}{21}$        $[Ans:\: 21x^{2}-15x+10]$

Q4- Find quotient and remainder on dividing P(x) and 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

Q5- If x + a is the factor of 2x2 + 2ax + 5x + 10, then find a

[Ans a = 2]

Q6) For what value of k,  -4 is a zero of the polynomial  x2 – x - (2k + 2) ?

[Ans k = 9]

Q7) - Find a if 2x - 3 is a factor of 6x³ - x² - 10x + a.

[Ans; a = - 3]

Q8)  Find a and b so that x⁴ + x³ + 8x² + ax - b is divisible by x² + 1.

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

Q9)  For what value of k is -3 a zero of x² + 11x + k.

Q10)  If 1 is the zero of ax² - 3(a - 1)x - 1 then find a.

Ans; a = 1

## LEVEL - 2

Q11)  Is (x + 2) a factor of 2x² + 3x + 1.

Q 12)  If α, β are the zeroes of P(x) = ax² + bx + c then find

a)   $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$        $\left [ Ans:\: \frac{b^{2}-2ac}{ac} \right ]$

b)  $\alpha ^{2}+\beta ^{2}$       $\left [ Ans:\: \frac{b^{2}-2ac}{a^{2}} \right ]$

c)   $\alpha ^{3}+\beta ^{3}$       $\left [ Ans:\: \frac{3abc-b^{3}}{a^{3}} \right ]$

d)   $\frac{1}{\alpha ^{3} }+\frac{1 }{\beta ^{3} }$      $\left [ Ans:\: \frac{3abc-b^{3}}{c^{3}} \right ]$

e)   $\frac{\alpha ^{2}}{\beta }+\frac{\beta ^{2}}{\alpha }$      $\left [ Ans:\: \frac{3abc-b^{3}}{a^{2}c} \right ]$

Q13- Verify that 1, 1/2, -2 are the zeroes of P(x) = 2x³ + x² - 5x + 2.

Q14- If the zeroes of x2 – Kx + 6 are in the ratio 3 : 2, find K

Q15. What is the degree of the polynomial (x + 1)(x2 – x - x4 + 1)

Q16- Find all zeroes of 2x³ + x² - 6x - 3 if its 2 zeroes are  ± $\sqrt{3}$

Q17- Find all the zeroes of  2x³ + x² - 5x + 2 if one of zero is 1/2.

Ans; 1, - 2

Q18- 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]

Q19) Obtain all zeroes of f(x) = x3 + 13x2 + 32x + 20, if one zero is -2

[Ans: All zeroes are  -10,  -1,  - 2]

Q20)  Find all the zeroes of 3x⁴ + 6x³ - 2x² - 10x - 5 if its two zeroes are  $\pm \sqrt{\frac{5}{3}}$

[Ans:  - 1, - 1]

Q21) Find all zeroes of 2x⁴ - 3x³ - 3x² + 6x - 2 if its two zeroes are   $\pm \sqrt{2}$

[Ans: 1]

Q22) Obtain all zeroes of f(x) = 2x4 - 2x3 - 7x2 + 3x + 6, if its two zeroes are  $\pm \sqrt{\frac{3}{2}}$     [Ans:  2, -1]

Q23) 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]

Q24) Find all zeroes of P(x) = x⁴ + x³ - 23x² - 3x + 60 if its 2 zeroes are   $\pm \sqrt{3}$

Q25)  Find all zeroes of P(x) = x⁴ + x³ - 34x² - 4x + 120 if its two zeroes are  ± 2,     [Ans; 5, - 6]

Q26)  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]

Q27- 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]

Q28- If one zero of the P(x) = 5x² + 13x + k is the reciprocal of the other then the value of k is?

[Ans; 5]

Q29- What must be subtracted from 8x⁴ + 14x³ - 2x² + 7x - 8 so that the resulting polynomial is divisible by  4x² + 3x - 2.

[Ans; 14x - 10]

Q30) What must be subtracted from z⁵ - 9z + 6 so that it is exactly divisible by z² + 3.

[ Ans; 6]

Q31)  What must be added to the polynomial p(x) = x4 + 2x3 - 13x2 - 12x + 21 so that the resulting polynomial is exactly divisible by x2 - 4x + 3

[Ans:   - 2x + 3]

Q32- What must be added to x⁴ + 2x³ - 2x² - x - 2 so that the resulting polynomial is  divisible by  x² + 2x - 3.

[Ans; 3x - 1]

Q33 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]

Q34- If α, β are the zeroes of P(y) = 2y² + 7y + 5 then find α + β +  αβ.

Q35. A polynomial P(x) is divisible by  (x - 4) and 2 is the zero of P(x), then write the corresponding polynomial.

Q36)  If α, β are the zeroes of P(x) = x- 5x + 4, then find the value of

a)   $\frac{1}{\alpha }+\frac{1}{\beta }$     $\left [Ans:\: \frac{-27}{4} \right ]$

b)   $\alpha ^{4}\beta ^{3}+\alpha ^{3}\beta ^{4}$     [Ans:  320]

Q37)  If α, β  are the zeroes of P(x) = x2 - 1, then find a quadratic polynomial whose zeroes are $\frac{2\alpha }{\beta }\: and\: \frac{2\beta }{\alpha }$

Ans[x2 + 4x + 4]

Q38.  If α, β are the zeros of the polynomial 25p2 – 15p + 2, then find a quadratic polynomial whose zeroes are   $\frac{1 }{2\alpha }+ \frac{1 }{2\beta }$

Q39) If α, β are the zeroes of  4x2 + 4x + 1, then form a quadratic polynomial whose zeroes are  2α, 2β

Q40) Find k so that x2 + 2x + k is a factor of  2x4 + x3 – 14x2 + 5x + 6

Ans[k = - 3, - 1]

Q41) 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]

Q42) Using division algorithm show that 6y5 + 15y4 + 16y3 + 4y2 + 10y – 35  is divisible by  3y2 + 5

Q43) On dividing the polynomial 9x4 – 4x2 + 5 by 3x2 + x - 1   remainder is ax - b. Find a and b

Q 44) If one zero of  (a2 + 9) x2 + 13x + 6a  is the reciprocal of the other then find the value of a

Q45) If sum of zeroes of ky2 + 2y – 3k  is equal to the twice their product , find the value of k

Q 46) If  α, β  are the zeroes of  P(x) = x2 – x – k  such that α – β  = 9, find the value of k.

## LEVEL - 3

Q 47)  If p and q are the zeroes of 2x2 – 7x + 3 then find the value of p2 + q2

Q 48) A quadratic polynomial 2x2 - 3x + 1 has zeroes as . Now form the quadratic polynomial whose zeroes are  3α and  3β

Q 49) Polynomial x4 + 7x3 + 7x2 + px + q  is exactly divisible by x2 + 7x + 12, then find the value of p and q .

Q 50) If α, β are the zeroes of  x2 + 4x + 3, find the polynomial whose zeroes are  $1+\frac{\beta }{\alpha }$  and  $1+\frac{\alpha }{\beta }$

Q 51) If x - $\sqrt{5}$   is the factor of x3 - 3 $\sqrt{5}$ x2 - 5x + 15$\sqrt{5}$  then find all zeroes of this polynomial.

Q 52) If x3 + 8x2 + kx + 18 is divisible by x2 + 6x + 9 then find the value of k.

Q 53) If 3x4 – 9x3 + x2 + 15x + k is divisible by 3x2 - 5 , find the value of k and other two zeroes  of the polynomial .

Q 54) On dividing x3 - 8x2 + 20x - 10 by g(x)  the quotient and remainder were x - 4 and 6 respectively . Find g(x)

Q 56) Find all zeroes of x4 - 17x2 - 36x - 20, if two of its zeroes are  5 and  -2

Q 57)  Find all zeroes of  x4 – 3  x3 + 3x2 + 3  x - 4 if two of its zeroes are $\sqrt{2}$ and 2$\sqrt{2}$

Q 58) What must be added or subtracted to 8x4 + 14x3 - 2x2 + 8x - 12 so that 4x2 + 3x - 2 is a factor of p(x).

Q 59) For what value of p, - 4 is the zero of P(x) = x2 - 2x - (7p + 3)

Q 60) If x4 + 2x3 + 8x2 + 12x + 18 is divided by another polynomial x2 + 5, the remainder is px + q . Find the value of p and q .

Q 61)  Find a quadratic polynomial whose zeroes are   $\frac{3\pm \sqrt{5}}{5}$

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