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This mock test of Practice Test: Polynomials for Class 10 helps you for every Class 10 entrance exam.
This contains 15 Multiple Choice Questions for Class 10 Practice Test: Polynomials (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The zeros of the quadratic polynomial x^{2} + ax + h, a,b > 0 are

Solution:

**The correct answer is b**

**Given quadratic polynomial is,**

**p(x)=x2+ax+b**

**Let one of the zero of the polynomial is a then the other zero will be −a.**

**Sum of zeros=a+(−a)= −a / 1**

**=>0= −a/1**

**=>a=0**

**and product of the zeros =a(−a)=b/1**

**=>−a2=b**

**=>b=−a2**

**=>b has to be negative.**

QUESTION: 2

If p(x) = ax^{2} + bx + c and a + b + c = 0, then one zero is

Solution:

QUESTION: 3

Given that one of the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d is zero, the product of the other two zeros is

Solution:

One zero = 0 (given)

Sum of roots in cubic polynomial = -b/a

0 + beta + gama = - ( -b )/a

beta + gama = b/a

Now, beta × gama = c/a

So, product of two zeroes = c/a

QUESTION: 4

If p(x) = ax^{2} + bx + c and a + c = b, then one of the zeroes is

Solution:

QUESTION: 5

If one of the zeros of the quadratic polynomial (k - 1) x^{2} + k x + 1 is - 3, then the value of k is

Solution:

QUESTION: 6

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

Solution:

QUESTION: 7

If one of the zeros of the cubic polynomial x^{3} + ax^{2} + bx + c is - 1, then the product of the other two zeroes is

Solution:

QUESTION: 8

Given that one of the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d is zero, the product of the other two zeroes is

Solution:

QUESTION: 9

Given that two of the zeros of the cubic polynomial ax^{3} + bx^{2} + cx + d are 0, the value of c is

Solution:

QUESTION: 10

If 4x^{2} - 6x - m is divisible by x - 3, the value of m is exact divisor of

Solution:

Here p(3) = 0

⇒ 4(3)^{2} - 6 x 3 - m = 0

⇒ 36 - 18 - m = 0 ⇒ m =18

∴ Value of m is exactly divisible by 9.

QUESTION: 11

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

Solution:

QUESTION: 12

Which one of the following statements is correct

Solution:

QUESTION: 13

The zeros of the quadratic polynomial x^{2} + kx + k, k ≠ 0

Solution:

QUESTION: 14

Consider the following statements

(i) x - 2 is a factor of x^{3} - 3x^{2} + 4x - 4.

(ii) x + 1 is a factor of 2x^{3} + 4x + 6

(iii) x - 1 is a factor of x^{5} + x^{4} - x^{3} + x^{2} - x + 1

In these statements

Solution:

x - 2 is a factor of x^{3} - 3x^{2} + 4x - 4

∵ remainder is zero

Similarly x + 1 is a factor of 2x^{3} + 4x + 6

but x - 1 is not a factor of x^{5} + x^{4} - x^{3} + x^{2} - x + 1

∵ remainder is not zero

∴ Statements 1 and 2 are correct.

QUESTION: 15

The degree of the remainder r(x) when p (x) = bx^{3} + cx + d is divided by a polynomial of degree 4 is

Solution:

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