**Class 10 Maths MCQs for chapter 2 Polynomials** are available here online, along with answers. These objective questions have been prepared, as per the CBSE syllabus (2022-2023) and NCERT curriculum. MCQ questions for Class 10 Maths are prepared as per the latest exam pattern. Practising these multiple-choice questions will help students to score better marks in their upcoming board exams. To practise MCQs for all the chapters, click here. Students can download the PDF to get more MCQs and solve them.

## Class 10 Maths MCQs for Polynomials

Class 10 Maths datasheet has been released by the CBSE board. MCQs for Chapter 2 polynomials are given here for Class 10 students for their revision. It will help them to increase their problem-solving skills. Later, they can verify their answers with the help of detailed explanations given here. Get important questions for class 10 Maths here at GMS.

Below are the MCQs for Chapter 2-Polynomials

**1. The zeroes of x ^{2}–2x –8 are:**

(a) (2,-4)

(b) (4,-2)

(c) (-2,-2)

(d) (-4,-4)

Answer: **(b) (4,-2)**

Explanation: x^{2}–2x –8 = x^{2}–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) 3x^{2}-3√2x+1

(b) 3x^{2}+3√2x+1

(c) 3x^{2}+3√2x-1

(d) None of the above

Answer: **(a) 3x ^{2}-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;

x^{2}–(α+β)x +αβ

= x^{2} –(√2)x + (1/3)

= 3x^{2}-3√2x+1

**3. If the zeroes of the quadratic polynomial ax ^{2}+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.

b^{2} -4ac = 0

b^{2} = 4ac

ac = b^{2}/4

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

**4. The degree of the polynomial, x ^{4} – x^{2} +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 x ^{3}+ax^{2}+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) = x^{3}+ax^{2}+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 x^{3}

(-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 x^{2}-3x-10, 2x^{2}-6x-20, (1/2)x^{2}-(3/2)x-5, 3x^{2}-9x-30, have zeroes as -2 and 5.

**10. Zeroes of p(x) = x ^{2}-27 are:**

(a) ±9√3

(b) ±3√3

(c) ±7√3

(d) None of the above

Answer: **(b) ±3√3**

Explanation: x^{2}-27 = 0

x^{2}=27

x=√27

x=±3√3

**11. Given that two of the zeroes of the cubic polynomial ax**^{3}** + bx**^{2}** + 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 x ^{2}**

**+ 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 x^{2} + 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 x ^{2}**

**+ 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 x^{2} + 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 x ^{2}**

**+ 7x + 10 are**

(a) -4, -3

(b) 2, 5

(c) -2, -5

(d) -2, 5

Answer:** (c) -2, -5**

Explanation:

x^{2} + 7x + 10 = x^{2} + 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 ax ^{3}**

**+ bx**

^{2}**+ 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 ax^{3} + bx^{2} + 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.