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Practice Test: Polynomials - Class 10 MCQ


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15 Questions MCQ Test Mathematics (Maths) Class 10 - Practice Test: Polynomials

Practice Test: Polynomials for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Practice Test: Polynomials questions and answers have been prepared according to the Class 10 exam syllabus.The Practice Test: Polynomials MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Practice Test: Polynomials below.
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Practice Test: Polynomials - Question 1

The zeroes of the quadratic polynomial x2 + ax + b, a,b > 0 are

Detailed Solution for Practice Test: Polynomials - Question 1

Practice Test: Polynomials - Question 2

If p(x) = ax2 + bx + c and a + b + c = 0, then one zero is

Detailed Solution for Practice Test: Polynomials - Question 2

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Practice Test: Polynomials - Question 3

Given Expression bx2 + cx + d  the product of the zeros is

Detailed Solution for Practice Test: Polynomials - Question 3

product of zero =  constant term / coefficient of x2
                         =  d/b 

Practice Test: Polynomials - Question 4

If p(x) = ax2 + bx + c and a + c = b, then one of the zeroes is

Detailed Solution for Practice Test: Polynomials - Question 4

Practice Test: Polynomials - Question 5

If one of the zeros of the quadratic polynomial  (k - 1) x2 + k x + 1 is - 3, then the value of k is

Detailed Solution for Practice Test: Polynomials - Question 5

Given, the quadratic polynomial is (k-1) x² + k x + 1.

One zero of the polynomial is -3.

Explanation:

Let f(x) = (k-1) x² + k x + 1

f(-3) = 0

Put x = -3 in the given polynomial

(k-1) (-3)² + k (-3) + 1 = 0

(k-1)(9) - 3k + 1 = 0

9k - 9 - 3k + 1 = 0

By grouping,

9k - 3k - 9 + 1 = 0

6k - 8 = 0

6k = 8

k = 8/6

k = 4/3

Therefore, the value of k is 4/3.

Practice Test: Polynomials - Question 6

The number of polynomials haying zeroes as -2 and 5 is

Detailed Solution for Practice Test: Polynomials - Question 6

 

⇒ p(x) = x2−3x−10
But we know that, if we multiply or divide any polynomial by any arbitrary constant. Then, the zeroes of the polynomial never change.
Therefore,

p(x)=kx2−3kx−10

 Where,k is a real number

Hence, the required number of polynomials having zeros −2 and 5 are infinite i.e. more than 3.

Practice Test: Polynomials - Question 7

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

Detailed Solution for Practice Test: Polynomials - Question 7

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

Practice Test: Polynomials - Question 8

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is

Detailed Solution for Practice Test: Polynomials - Question 8

Let p(x) =ax3 + bx2 + cx + d
Given that, one of the zeroes of the cubic polynomial p(x) is zero.
Let α, β and γ are the zeroes of cubic polynomial p(x), where a = 0.
We know that,

Practice Test: Polynomials - Question 9

Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, the value of c is

Detailed Solution for Practice Test: Polynomials - Question 9

Explanation:

Given Information:
- Two zeros of the cubic polynomial are 0.
- Therefore, the cubic polynomial can be written as ax^3 + bx^2 + cx + d = a(x - 0)(x - 0)(x - k) = ax^3 - akx^2 = ax^3.

Finding the value of c:
- Since the coefficient of the linear term in the polynomial is c, and two of the zeros are given to be 0, the sum of the zeros is 0 + 0 + k = -b/a.
- As k represents the remaining zero, this implies that k = -b/a.
- Since the sum of the zeros of a cubic polynomial is -b/a, the value of c cannot be determined from the given information.
- Therefore, the correct answer is c.​​​​

Practice Test: Polynomials - Question 10

If 4x2 - 6x - m is divisible by x - 3, the value of m is exact divisor of

Detailed Solution for Practice Test: Polynomials - Question 10

Here p(3) = 0
⇒ 4(3)2 - 6 x 3 - m = 0
⇒ 36 - 18 - m = 0 ⇒ m =18
∴ Value of m is exact divisior of 36.

Practice Test: Polynomials - Question 11

A quadratic polynomial, whose zeros are 5 and - 8 is

Detailed Solution for Practice Test: Polynomials - Question 11

x2 - (sum of roots)x + product of roots
x2 - (5+(-8))x + 5x-8
x2​​​​​​​ - (-3)x + -40
x2​​​​​​​ + 3x -40
 

Practice Test: Polynomials - Question 12

Which one of the following statements is correct

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Practice Test: Polynomials - Question 13

The zeros of the quadratic polynomial x2 + kx + k, k ≠ 0

Practice Test: Polynomials - Question 14

Consider the following statements
(i) x - 2 is a factor of x3 - 3x2 + 4x - 4.
(ii) x + 1 is a factor of 2x3 + 4x + 6
(iii) x - 1 is a factor of x5 + x4 - x3 + x2 - x + 1

In these statements

Detailed Solution for Practice Test: Polynomials - Question 14

x - 2 is a factor of x3 - 3x2 + 4x - 4
∵ remainder is zero
Similarly x + 1 is a factor of 2x3 + 4x + 6
but x - 1 is not a factor of x5 + x4 - x3 + x2 - x + 1
∵ remainder is not zero
∴ Statements 1 and 2 are correct.

Practice Test: Polynomials - Question 15

The degree of the remainder r(x) when p (x) = bx3 + cx + d is divided by a polynomial of degree 4 is ​

Detailed Solution for Practice Test: Polynomials - Question 15

as degree of divisor is 4 which is greater than dividend so reaminder would itself be dividend as division cannot occur so degree of remainder would be 3

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