Class 10 Maths Chapter 2 Polynomials MCQs

We have provided here MCQs for Class 10 Maths chapter Polynomials online, along with answers. These objective questions have been prepared, as per the CBSE syllabus and NCERT curriculum. Practising these multiple-choice questions will help students to score better marks in the board exams. It will help them to increase their problem-solving skills. To practice MCQs for all the chapters, click here.

Class 10 Maths MCQs for Polynomials

MCQs for polynomials are given here for Class 10 students and they are advised to solve these questions as per their knowledge and skills. Later, they can verify their answers with the help of detailed explanations given here. Get important questions for class 10 Maths here at BYJU’S.

Click here to download the PDF of additional MCQs for Practice on Polynomials Chapter of Class 10 Maths along with answer key:

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Students can also get access to Polynomials Class 10 Notes here.

Below are the MCQs for Chapter 2-Polynomials

1. The zeroes of x2–2x –8 are:

(a) (2,-4)

(b) (4,-2)

(c) (-2,-2)

(d) (-4,-4)

Answer: (b) (4,-2)

Explanation: x2–2x –8 = x2–4x + 2x –8

= x(x–4)+2(x–4)

= (x-4)(x+2)

Therefore, x = 4, -2.

2. What is the quadratic polynomial whose sum and the product of zeroes is √2, ⅓ respectively?

(a) 3x2-3√2x+1

(b) 3x2+3√2x+1

(c) 3x2+3√2x-1

(d) None of the above

Answer: (a) 3x2-3√2x+1

Explanation: Sum of zeroes = α + β =√2

Product of zeroes = α β = 1/3

∴ If α and β are zeroes of any quadratic polynomial, then the polynomial is;

x2–(α+β)x +αβ

= x2 –(√2)x + (1/3)

= 3x2-3√2x+1

3. If the zeroes of the quadratic polynomial ax2+bx+c, c≠0 are equal, then

(a) c and b have opposite signs

(b) c and a have opposite signs

(c) c and b have same signs

(d) c and a have same signs

Answer: (d) c and a have same signs

Explanation:

For equal roots, discriminant will be equal to zero.

b2 -4ac = 0

b2 = 4ac

ac = b2/4

ac>0 (as square of any number cannot be negative)

4. The degree of the polynomial, x4 – x2 +2 is

(a) 2

(b) 4

(c) 1

(d) 0

Answer: (b) 4

Explanation: Degree is the highest power of the variable in any polynomial.

5. If one of the zeroes of cubic polynomial is x3+ax2+bx+c is -1, then product of other two zeroes is:

(a) b-a-1

(b) b-a+1

(c) a-b+1

(d) a-b-1

Answer: (b) b-a+1

Explanation: Since one zero is -1, hence;

P(x) = x3+ax2+bx+c

P(-1) = (-1)3+a(-1)2+b(-1)+c

0 = -1+a-b+c

c=1-a+b

Product of zeroes, αβγ = -constant term/coefficient of x3

(-1)βγ = -c/1

c=βγ

βγ = b-a+1

6. If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:

(a) Zero of p(x)

(b) Value of p(x)

(c) Constant of p(x)

(d) None of the above

Answer: (a) Zero of p(x)

Explanation: Let p(x) = mx+n

Put x = a

p(a)=ma+n=0

So, a is zero of p(x).

7. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial is:

(a) Intersects x-axis

(b) Intersects y-axis

(c) Intersects y-axis or x-axis

(d) None of the above

Answer: (a) Intersects x-axis

8. A polynomial of degree n has:

(a) Only one zero

(b) At least n zeroes

(c) More than n zeroes

(d) At most n zeroes

Answer: (d) At most n zeroes

Explanation: Maximum number of zeroes of a polynomial = Degree of the polynomial

9. The number of polynomials having zeroes as -2 and 5 is:

(a) 1

(b) 2

(c) 3

(d) More than 3

Answer: (d) More than 3

Explanation: The polynomials x2-3x-10, 2x2-6x-20, (1/2)x2-(3/2)x-5, 3x2-9x-30, have zeroes as -2 and 5.

10. Zeroes of p(x) = x2-27 are:

(a) ±9√3

(b) ±3√3

(c) ±7√3

(d) None of the above

Answer: (b) ±3√3

Explanation: x2-27 = 0

x2=27

x=√27

x=±3√3

11. Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, the third zero is

(a) -b/a

(b) b/a

(c) c/a

(d) -d/a

Answer: (a) -b/a

Explanation:

Let α be the third zero.

Given that two zeroes of the cubic polynomial are 0.

Sum of the zeroes = α + 0 + 0 = -b/a

α = -b/a

12. If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is

(a) 10 

(b) –10 

(c) 5 

(d) –5

Answer: (b) -10

Explanation:

Given that 2 is the zero of the quadratic polynomial x2 + 3x + k.

⇒ (2)2 + 3(2) + k = 0

⇒ 4 + 6 + k = 0

⇒ k = -10

13. A quadratic polynomial, whose zeroes are –3 and 4, is

(a) x² – x + 12 

(b) x² + x + 12

(c) (x²/2) – (x/2) – 6

(d) 2x² + 2x – 24

Answer: (c) (x²/2) – (x/2) – 6

Explanation:

Let the given zeroes be α = -3 and β = 4.

Sum of zeroes, α + β= -3 + 4 = 1 

Product of Zeroes, αβ = -3 × 4 = -12 

Therefore, the quadratic polynomial = x² – (sum of zeroes)x + (product of zeroes) 

= x² – (α + β)x + (αβ) 

= x² – (1)x + (-12) 

= x² – x – 12

Dividing by 2,

= (x²/2) – (x/2) – 6

14. The zeroes of the quadratic polynomial x2 + 99x + 127 are

(a) both positive 

(b) both negative

(c) one positive and one negative 

(d) both equal

Answer: (b) both negative

Explanation:

Given quadratic polynomial is x2 + 99x + 127.

By comparing with the standard form, we get;

a = 1, b = 99 and c = 127

a > 0, b > 0 and c > 0

We know that in any quadratic polynomial, if all the coefficients have the same sign, then the zeroes of that polynomial will be negative.

Therefore, the zeroes of the given quadratic polynomial are negative.

15. The zeroes of the quadratic polynomial x2 + 7x + 10 are

(a) -4, -3

(b) 2, 5

(c) -2, -5

(d) -2, 5

Answer: (c) -2, -5

Explanation:

x2 + 7x + 10 = x2 + 2x + 5x + 10

= x(x + 2) + 5(x + 2)

= (x + 2)(x + 5)

Therefore, -2 and -5 are the zeroes of the given polynomial.

16. If the discriminant of a quadratic polynomial, D > 0, then the polynomial has

(a) two real and equal roots

(b) two real and unequal roots

(c) imaginary roots

(d) no roots

Answer: (b) two real and unequal roots

If the discriminant of a quadratic polynomial, D > 0, then the polynomial has two real and unequal roots.

17. If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, then the relation between the degrees of p(x) and g(x) is

(a) degree of p(x) < degree of g(x)

(b) degree of p(x) = degree of g(x)

(c) degree of p(x) > degree of g(x) 

(d) nothing can be said about degrees of p(x) and g(x)

Answer: (a) degree of p(x) < degree of g(x)

Explanation:

We know that, p(x)= g(x) × q(x) + r(x) 

Given that, q(x) = 0 

When q(x) = 0, then r(x) = 0

So, now when we divide p(x) by g(x),

Then p(x) should be equal to zero.

If r(x) = 0, then the degree of p(x) < degree of g(x).

18. By division algorithm of polynomials, p(x) =

(a) g(x) × q(x) + r(x)

(b) g(x) × q(x) – r(x)

(c) g(x) × q(x) × r(x)

(d) g(x) + q(x) + r(x)

Answer: (a) g(x) × q(x) + r(x)

By division algorithm of polynomials, p(x) = g(x) × q(x) + r(x).

19. The product of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is

(a) -b/a

(b) c/a

(c) -d/a

(d) -c/a

Answer: (c) -d/a

The product of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is -d/a.

20. If the graph of a polynomial intersects the x-axis at three points, then it contains ____ zeroes.

(a) Three

(b) Two

(c) Four

(d) More than three

Answer: (a) Three

 If the graph of a polynomial intersects the x-axis at three points, then it contains three zeroes.

12 Comments

  1. This mcq questions are very easy but very useful for exam

  2. Very hard but interesting question

  3. You’re app is the best app

  4. Very nice questions

  5. If the zeroes of the quadratic polynomial X2+bx+c, c#0 are equal then

    1. If the zeroes of the quadratic polynomial ax^2+bx+c, c≠0 are equal then,
      b^2-4ac = 0
      b^2 = 4ac
      Since, b^2 cannot be negative therefore, a and c are also not negative.

  6. I want class 10 maths important MCQ S questions for all chapters

    1. Click here, to find the Class 10 MCQs for all the chapters.

  7. Zeroes of P(x) = x² – 2x – 3 are

    1. P(x) = x² – 2x – 3
      Factoring the given expression, we get;
      x² – 3x + x – 3
      = x(x – 3) + 1(x – 3)
      = (x – 3)(x + 1)
      To find the zeroes of P(x);
      P(x) = 0
      (x – 3)(x + 1) = 0
      x = 3 or x = -1
      Thus, the zeroes are 3 and -1.

    2. Zeroes of P(x) = x² – 2x – 3 are 3 and -1

  8. Pretty good questions

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