Polynomials Class 10 MCQ with Answers

Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test are covered in this Article. Polynomials Class 10 MCQ Test contains 30 questions. Answers to MCQs on Polynomials Class 10 MCQ with Answers Maths are available at the end of the last question. These MCQ have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.

Board CBSE
Textbook Maths (NCERT)
Class Class 10
Chapter Chapter 2 Polynomials
Category MCQ Questions for Class 10 Maths with Answers

Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

1. The graphical representation of Quadratic polynomial is
a)  Straight line
b) Quarter graph
c) Parabolic
d) Composite graph

2. The degree of the polynomial (x² – 1)(x³– x4– x +1) is
a) 3
b) 4
c) 5
d) 6

3. The graph represents how many zeroes

a) 3
b) 2
c) 1
d) 0

4. The zeroes of the quadratic polynomial x² + 4x +4 are
a) both positive
b) both negative
c) one positive and one negative
d) both equal

5. Parabola in the given figure opens

a) Concave upward
b) Concave downward
c) Concave left
d) Concave right

6. The zeroes of polynomial depends on its
a) No. Of terms
b) Degree
c) Both
d) None




7. If α and β are the zeroes of the polynomial  x²-7x +12, Find the value of √( α²+ β²) is
a) 2
b) 3
c) 4
d) 5

8. The polynomial of degree 3 has at most how many zeroes
a) 3
b) 2
c) 1
d) 0

9. The zeroes of the quadratic polynomial 6x² + 11x – 35 are
a) both positive
b) both negative
c) one positive and one negative
d) both equal

10. If the zeroes of the quadratic polynomial x² – ax + b are 5 and –7, then
a) a = –2, b = –10
b) a = 5, b = –10
c) a = -2, b = –35
d) a = 7, b = – 6

Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

11. A quadratic polynomial, whose zeroes are -1and 2, is
a) ( x²- x + 2)
b) x² +x -2
c) x² -x -2
d) x²+2x – 2

12. Given that the two zeroes of cubic polynomial 3x³+2x²+x+1 are 0, then the third zero is
a) -2/3
b) -1/3
c) 3/2
d) 0

13. If α and β are the zeroes of the polynomial  3x² -9x +12, Find the value of ( α + β)
a) 1
b) 3
c) 2
d) 4

14.If (bx²+cx + a) is quadratic polynomial having c ≠ 0 are equal and all zero are equal then
a) a and b have opposite signs
b) a and c have opposite signs
c) a and b have the same sign
d) a and c have the same sign

15. A quadratic polynomial whose one zero is 5 and sum of the zeroes is 0, is
a) X²-7x+2
b) X² -25
c) X²-5
d) X²+5x+1

16. A quadratic polynomial whose product of zeroes is 3 and sum of the zeroes is 4
a) X² – 4x+3
b) X² – 16
c) X²-7x+2
d) X²+3x+4

17. Given that two of the zeroes of the cubic polynomial 4x³+5x²+6x+ 1 are 0, the third zero is
a) 6
b) 6/4
c) -5/4
d) 1

18. The number of polynomials having exactly two zeroes 2 and -1 is
a) 1
b) 2
c) 3
d) infinite




19. Parabola facing downwards indicates
a) a<0
b) a>0
c) a=0
d) a#0

20. The quadratic polynomial ax²+ bx + c has no real zero in which case
a) the graph completely above the x-axis
b) the graph completely below the x-axis
c) Both a and b
d) None of the above

21. The graph having atmost 3 zeroes

a) a
b) b
c) c
d)d

22. If one of the zeroes of the quadratic polynomial (k+1) x² + kx + 1 is – 3, then the value of k is
a) 4
b) 3/5
c) -5/3
d) -5

23. If one of the zeroes of the cubic polynomial x³+ ax² + bx + c is zero, the product of the other two zeroes is
a) a
b) b
c) c
d) 0

24. Given the two zeroes of cubic polynomial  ax³+3x²-bx-6 are -1 and -2, find the value of a and b
a) a= 5, b=2
b) a =3, b=4
c) a =2, b= 5
d) a = -3, b=2

25. Find the third zero of cubic polynomial 2x³+3x²-5x-6 , where the other two zeroes are -1 and -2.
a) 3/2
b) -2/3
c) -5/2
d) 5/3

26. If α and β are the zeroes of quadratic polynomial x2+x-6, then
a) α +β =αβ
b) α – β =αβ
c) α +β >αβ
d) α +β <αβ

27. The graph of polynomial 3x-15 intersects x-axis at
a) 5,0
b) 0,5
c) -5,0
d) 0,-5

28. If α and β are the zeroes of quadratic polynomial x²+x-6, then find α – β.
a) 2
b) 3
c) 5
d) 7

29. The graph of cubic polynomial 2x³-3 meets the x-axis at (0,-3), (1, -1),(-1, -5),find the zeroes of polynomial
a) -3,-1,-5
b) -2,-1,-5
c) 0,2,-1
d) 0,1,-1

30. If α and β are zeroes of polynomial 3x²-4x+4, then find α+β+αβ
a) -4/3
b) 3/4
c) 8/3
d) 2/3




Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

Correct Answers

1. Answer: C

2. Answer:  D

Solution: The highest degree variable in first bracket is x² and in second bracket is x⁴ on multiplying x² with x⁴. the highest power we obtain is 6.

3. Answer: B

Solution: The graph represents quadratic polynomial which intersects the x-axis at two points ,thus having 2 zeroes.

4. Answer: B

Solution: p(x)=x2 + 4x +4
x² + 4x +4 =0
x² + 2x +2x+4=0
x(x+2)+2(x+2)=0
(x+2)(x+2)=0
X= -2; -2

5. Answer: A

6. Answer: B

Solution:

polynomial degree zeroes
Linear 1 1
Quadratic 2 2
Cubic 3 3

…so on.

7. Answer: D
Solution: p(x) = x²-7x +12
x²-7x +12 =0
x²-4x -3x +12=0
X(x-4) -3(x-4) =0
(x-4)(x-3)=0
X =4; 3

If α=4; β=3
Then, √α2+β2
=√16+9
=√25
=5

8. Answer: A

9. Answer: C
Solution: p(x)= 6x² + 11x – 35
6x² + 11x – 35 =0
6x² + 21x – 10x – 35 =0
3x(2x+7) -5(2x+7) =0
(2x+7)(3x-5)=0
X= -7/2 ; 5/3

10. Answer:  D
Solution: α=5; β=-7
α+β= -b/a
5+(-7)= -(-a)/1
5-7=a
a = -2
αβ= c/a
5x(-7)=b/1
b = -35
Hence, a= -2; b = -35

Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

11. Answer: C
Solution:  α= -1 ; β= 2
(X-α) (x-β)is   the  quadratic   polynomial having zeros as -1 & 2 .
{(x—(-1)} (x-2)
(x+1) (x-2)
=x² -2x+x-2
= x² -x -2

12. Answer: A
Solution: α=0, β=0, γ=?
α+β+γ= -b/a
0+0+γ= -2/3
γ= -2/3




13. Answer: B
Solution:  3x² -9x +12 indicate as a=3; b=-9 c=12
Sum of Zeros(α+β) = -b / a
= -(-9) / 3
= 3

14. Answer: C
Solution: The zeroes of the quadratic polynomial ax² + bx + c , c ≠ 0 are equal
Value of discriminant (D) has to be zero
b² – 4ac = 0
b² = 4ac
Here,
c²  = 4ba
c² /4  = ba
Since L.H.S. ( c² /4 ) can never be negative
R.H.S. also can never be negative.
a and b must have same sign

15. Answer: B
Solution: α= 5; α+β =0
Then, β= -5
Formed polynomial will be,
(x-α)(x-β)
=(x-5)(x+5)
=x²-25

16. Answer: A
Solution:
α+β= 4;
-b/a= 4
-b/a= -(-4)/1
αβ =3
c/a = 3
c/a = 3/1
Therefore, a = 1, b = -4, c =3

Formed quadratic,
x²-4x+3

17. Answer: C
Solution: α+β+γ = -b/a
0+0+γ = -5/4
γ = -5/4

18. Answer : D
Solution: The formed quadratic polynomial having exactly two zeroes is infinite

19. Answer:   A
Solution: Whether the parabola is facing upwards or downwards, depends on the nature of a.
If a > 0, the parabola faces upward.
If a < 0, the parabola faces downwards.

20. Answer: C
Solution:  When the graph is either completely above the x-axis or completely below the x-axis, it does not cut the x-axis at any point. So, in this case, it does not have any real zeroes.

Polynomials Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

21. Answer: D
Solution: The graph (d) intersects the x-axis at 3 points.

22. Answer: C
Solution: α+β= -b/a
-3+ β = -k/k+1
β = 3-k/k+1
β = 3k+3-k/k+1
β=2k+3/k+1…………………..(i)
αβ = c/a
-3β = 1/k+1
β= -1/3(k+1)………………(ii)
From (i)and (ii),
2k+3/k+1=-1/3(k+1)
3(2k+3) = -1
6k + 9 = -1
6K = -10
K = -5/3

23. Answer: B
Solution: γ =0; αβ =?
αβ + βγ + γα = c/a
αβ = c/a
αβ = b/1 =b

24. Answer: C
Solution: α= -1; means p(-1)=0
β= -2; means p(-2)=0
P(-1)= -a+3+b-6=0
b -a=3………(i)
P(-2)= -8a+12+2b-6=0
2b -8a= -6…………(ii)
From (i) and (ii),
a =2 ; b= 5

25. Answer: A
Solution: αβγ= -c/a
(-1)(-2)γ= -(-6)/2
2γ=3
γ= 3/2

26. Answer: C
Solution: α +β =-b/a =-1/1 =-1
αβ = c/a = -6/1 = -6
Here, -1>-6

27. Answer: A
Solution: 3x -15=0
X=15/3 =5

28. Answer: C
Solution: α +β =-b/a =-1/1 =-1
αβ = c/a = -6/1 = -6
Using, (a-b)²=(a+b)²-4ab
(α – β)²= (α + β)² -4αβ
= (-1)²- 4(-6)
=  1+ 24
= 25
α – β = 5

29. Answer: D
Solution:  When the graph of cubic polynomial intersects the x-axis thrice, then the zeroes of cubic polynomial are the coordinates of the x-axis.

30. Answer: C
Solution: α + β = -b/a =- (-4)/3 = 4/3
αβ = c/a = 4/3
α+β+αβ = 4/3 + 4/3
= 8/3

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