**3. POLYNOMIALS**

Hi
friends and my dear students! In this post, I have covered **Important questions for 10 ^{th} class
maths chapter-3**

**polynomial**

**,Chapter wise previous year Questions.**After Reading Please do share it with your friends.

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PRIORITY-I

1 MARK QUESTIONS:

1. Give an example for

i) linear polynomial

ii) quadratic polynomial

iii)
Cubic polynomial

2. Write the general form of a first
degree polynomial in one variable x?

3. Define zeroes of polynomial?

4. If p(x) = 5x^{7} – 6x^{5}
+ 7x – 6 then find

i) coefficient of x^{5}?

ii) degree of p(x)?

iii. constant term.

5. Write the polynomial that has

i)1 zero ?

ii) 2 zeroes?

iii) no zero

6.
How will you verify if polynomial has only one zero?

7. Find the number of zeroes of

(i) 2x+1 (ii) x^{2} – 1
(iii) x^{3}

8. Find the sum of the zeroes and
product of zeroes of *ax*^{2} + *bx *+ *c? *

2 MARK QUESTIONS:

9. If p(x) = x^{2} – 5x –
6 the value of find p(0), p(1), p(2), p(3),p(-1),p(-2),p(-3)?

10. If p(m) = m^{2} – 3m
+ 1 find the value of p(1) and p(-1)?

11. Check whether -3 and 3 are the
zeroes of the polynomial x^{2} – 9?

12. Check whether -2 and 3 are the
zeroes of the polynomial p(x) = x^{2} -x– 6?

13. Find the zeroes of the polynomial
i) p(x) = x^{2} +5x +6 ii) p(x) = (x+2)(x-3) iii) p(x) = x^{4} –
16

14. Why are ¼ and –1 zeroes of the
polynomials *p(x) *= 4*x*^{2} + 3*x *– 1?

15. Find the zeroes of the polynomial
p(x) = x^{2 }+7x +10 and verify the relationship between the zeroes and
coefficients?

16. Draw the rough sketch of y=x^{3 }

17. Find the zeroes of the polynomial
p(x) = x^{2} - 3 and verify the relationship between the zeroes and
coefficients?

18. Find a quadratic polynomial, the
sum and product of whose zeroes are -3 and 2 respectively?

19. Find quadratic polynomial if the
zeroes of it are 2 and -1/3 respectively?

20. Divide 2x^{2 }+ 3x + 1 by x
+ 2?

21.
Divide 3x^{3} + x^{2} + 2x + 5 by 1+ 2x + x^{2}?

**Also Check**

**Introduction to Knowing Our Numbers Key Points**

**SSC (10th class) Trigonometry Exercise - 11.1 Solution**

**SSC(10th class) Trigonometry Exercise - 11.1 Solutions**

4 MARK QUESTIONS:

1. Draw the graphs of the given polynomial and find the zeroes.
Justify the answers.

(i) *p(x) *= *x*^{2} – *x *– 12 (ii) *p(x)
*= *x*^{2 }– 6*x *+ 9

(iii) *p(x) *= *x*^{2 }– 4*x *+ 5 (iv) *p(x)
*= *x*^{2} + 3*x-4 *(v) *p(x) *= *x*^{2}
– 1 (vi) *x*^{2 }– 3*x *– 4

2. Draw the graphs of (i) *y
*= *x*^{2} – *x *– 6 (ii) *y *= 6 – *x *– *x*^{2}
and find zeroes in each case. What do you notice?

3. Verify that 1, –1 and –3
are the zeroes of the cubic polynomial *x*^{3} + 3*x*^{2}
– *x *– 3 and check the relationship between zeroes and the coefficients

4. Find all the zeroes of 2*x*^{4 }– 3*x*^{3 }–
3*x*^{2} + 6*x *– 2, if you know that two of its zeroes are
and - √2, √2

1 MARK QUESTIONS:

1. Write the division
algorithm?

2. If R(x)=x^{2}-10x+40
then find R(1)+R(0)

3. Write the condition for
ax^{2}+bx+c is not to be a quadratic polynomial

4. Write the degree of i. x^{3}+7x^{2}+1
ii. x-x^{7}+3

5. Is 1/x-1a polynomial?
Justify your answer?

6. What is the degree of a
zero polynomial?

7. Find the product of
zeros of 2017 x^{2}-1

8. Find the sum and product
of the zeroes of p(x)=6x^{2}-7x+3

9. What is the shape of
graph of quadratic polynomial and linear polynomial?

10. When the upward parabola forms a quadratic polynomial graph?

11. Write a general polynomial of
degree ‘n’ with coefficients that are a_{0},a_{1}----a_{n }

12. If β,α are zeroes of the polynomial
2x^{2}+7x+5, find the value of β+α +βα

Also Check

**Important questions for 10th class maths chapter-1 Real numbers**

**Important questions for 10th class maths chapter-4**** **LINEAR EQUATIONS

2 MARK QUESTIONS:

1. Find the value of ‘k’ so that x^{3}-3x^{2}+4x+k
is exactly divisible by x-2

2. If are the zeros of p(x)=x^{3}+x^{2}+
2/3x+1 then find the βα + βδ +αδ

3. If β and α are the zeros of 2x^{2}+x-1
then find the value of 1/α+1/ β

4. If p(x)=3x^{2}+5x-6 then
find p(1) and p(2)

5. Find a quadratic polynomial with the
sum ¼ and product -1 of its zeros

6. Find the value of ‘m’ in order that
x^{4}- 2x^{3}+3x^{2}-mx+6 may be divisible by x-3

7. *If *β,α,δ are the zeroes of a
polynomial of degree 3, then give the relations between the zeroes and the
coeffients of the polynomial

4 MARKS QUESTIONS:

1. Draw the graph of y = x^{3}
- 4x, find the zero of y = x^{3} - 4x?

2. Verify that 3, –1, -1/3 are the
zeroes of the cubic polynomial *p(x) *= 3*x*^{3} – 5*x*^{2}
– 11*x *– 3, and then verify the relationship between the zeroes and the
coefficients

3. On dividing *x*^{3} – 3*x*^{2}
+ *x *+ 2 by a polynomial *g(x)*, the quotient and remainder were *x
*– 2 and – 2*x *+ 4, respectively. Find *g(x) *

4. Divide 3x^{2} – x^{3}
– 3x + 5 by x – 1 – x2, and verify the division algorithm?

5.
Obtain all other zeroes of 3*x*^{4 }+ 6*x*^{3} – 2*x*^{2
}– 10*x *– 5, if two of its zeroes are and – √5/3 ,√5/3

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