Class 10th Chapter Polynomial MCQs (Math)

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Books Guru Gyan providing you the Multiple Choice Questions (MCQs) of Chapter Polynomial of Class Xth. Scroll-Down to read the MCQs Online or Download Pdf.

Chapter Name : Real Numbers

Read this Book :

No. of Questions : 20

Questions

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.