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Test: Polynomials - 1


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25 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Polynomials - 1

Test: Polynomials - 1 for Class 9 2022 is part of Mathematics (Maths) Class 9 preparation. The Test: Polynomials - 1 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Polynomials - 1 MCQs are made for Class 9 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Polynomials - 1 below.
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Test: Polynomials - 1 - Question 1

A cubic polynomial is a polynomial with degree

Detailed Solution for Test: Polynomials - 1 - Question 1

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x) = a3 x3 + a2 x2 + a1 x + a0. An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.

Test: Polynomials - 1 - Question 2

A polynomial of degree 5 in x has at most

Detailed Solution for Test: Polynomials - 1 - Question 2

A polynomial of degree 5 is of the form p(x) =, where a, b, c, d, e, and f are real numbers and a ≠ 0.

Thus, p(x) can have at most 6 terms and at least one term containing

Test: Polynomials - 1 - Question 3

The coefficient of x3 in the polynomial 5 + 2x + 3x2 – 7x3 is

Test: Polynomials - 1 - Question 4

The quadratic polynomial whose sum of zeroes is 3 and the product of zeroes is –2 is :

Detailed Solution for Test: Polynomials - 1 - Question 4

Sum of zeros = 3/1 
-b/a = 3/1 .....................(1)

Product of zeros = -2/1
c/a = -2/1 ...................(2)

From equation (1) and (2)
a = 1
-b = 3, b = -3
c = -2

The required quadratic equation is 
ax^2+by+c
= x2-3x-2

Test: Polynomials - 1 - Question 5

A linear polynomial :-

Detailed Solution for Test: Polynomials - 1 - Question 5

A number of zeroes of an n -degree polynomial = n. 

First, a linear polynomial is in the form of ax + b, a≠0, a,b ∈R 

The degree of the polynomial = highest degree of the terms 
So here the highest degree is 1. 

Hence, Linear polynomial has only one zero.

Test: Polynomials - 1 - Question 6

If x + y = 3, x2 + y2 = 5 then xy is

Detailed Solution for Test: Polynomials - 1 - Question 6

Test: Polynomials - 1 - Question 7

When the polynomial x3 + 3x2 + 3x + 1 is divided by x + 1, the remainder is :-

Detailed Solution for Test: Polynomials - 1 - Question 7

The zero of x + 1 is –1

                And by remainder theorem, when

                p(x) = x3 + 3x2 + 3x + 1 is divided by x + 1, then remainder is p(–1).

                ∴ p(–1) = (–1)3 + 3 (–1)2 + 3(–1) + 1

                = –1 + (3 × 1) + (–3) + 1

                = –1 + 3 – 3 + 1

                = 0

                Thus, the required = 0

Test: Polynomials - 1 - Question 8

If the polynomial 2x3 – 3x2 + 2x – 4 is divided by x – 2, then the remainder is :-

Test: Polynomials - 1 - Question 9

The value of k for which x – 1 is a factor of the polynomial 4x3+ 3x2 – 4x + k is :-

Detailed Solution for Test: Polynomials - 1 - Question 9

X - 1 is a factor of 4x3 + 3x2 -4x +k
then x=1 is one root of 4x3 + 3x2 -4x +k

put x= 1
4x3 +3x2 -4x +k = 0

=> 4 (1)3 +3 (1)2-4 (1) +k =0

=> 4 + 3 - 4 + k = 0

=> k = -3 

Test: Polynomials - 1 - Question 10

The value of k for which x + 1 is a factor of the polynomial x3 + x2 + x + k is :-

Test: Polynomials - 1 - Question 11

The value of m for which x – 2 is a factor of the polynomial x4 – x3 + 2x2 – mx + 4 is :-

Test: Polynomials - 1 - Question 12

The factors of 2x2 – 3x – 2 are :-

Detailed Solution for Test: Polynomials - 1 - Question 12

2x2 – 3x – 2

2x2 - 4x + x - 2 = 0

2x2(x-2) +1(x-2) = 0

(2x+1) (x-2)

Test: Polynomials - 1 - Question 13

If x + 2 is a factor of x3 – 2ax2 + 16, then value of a is

Test: Polynomials - 1 - Question 14

The factors of x3 – 2x2 – 13x – 10 are :-

Test: Polynomials - 1 - Question 15

The expanded form of (2x – 3y – z)2 is :-

Test: Polynomials - 1 - Question 16

The expanded form of (x + y + 2z)2 is :-

Test: Polynomials - 1 - Question 17

The expanded form of (x+1/3)3 is :-  

Test: Polynomials - 1 - Question 18

x3 + y3 + z3 – 3xyz is :-

Detailed Solution for Test: Polynomials - 1 - Question 18

We know that x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx).
If x + y + z = 0, then x3 + y3 + z3 – 3xyz = 0 or x3 + y3 + z3 = 3xyz.

Test: Polynomials - 1 - Question 19

(a – b)3 + (b – c)3 + (c – a)3 is equal to :-

Detailed Solution for Test: Polynomials - 1 - Question 19

Let x = (a – b), y = (b – c) and z = (c – a)
Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0
⇒ x3 + y3 + z3 = 3xyz
That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)

Test: Polynomials - 1 - Question 20

 is equal to :-

Test: Polynomials - 1 - Question 21

√2 is a polynomial of degree

Detailed Solution for Test: Polynomials - 1 - Question 21

The highest power of the variable is known as the degree of the polynomial.

√2x^0 = √2
hence the degree of the polynomial is zero.

Test: Polynomials - 1 - Question 22

The degree of the polynomial 4x4+0x3+0x5+5x+74x4+0x3+0x5+5x+7 is

Detailed Solution for Test: Polynomials - 1 - Question 22

The degree of the polynomial 4x4+0x3+0x5+5x+74x4+0x3+0x5+5x+7 is

Test: Polynomials - 1 - Question 23

The degree of the zero polynomial is

Detailed Solution for Test: Polynomials - 1 - Question 23

The degree of zero polynomial is not defined, because, in zero polynomial, the coefficient of any variable is zero i.e., Oxor Ox5, etc. Hence, we cannot exactly determine the degree of the variable.  

Test: Polynomials - 1 - Question 24

The value of the polynomial 5x−4x2+3, when x = −1 is

Detailed Solution for Test: Polynomials - 1 - Question 24

 Let p (x) = 5x – 4x2 + 3 …(i)
On putting x = -1 in Eq. (i), we get
p(-1) = 5(-1) -4(-1)2 + 3= - 5 - 4 + 3 = -6

Test: Polynomials - 1 - Question 25

If p(x) = x + 3, then p(x) + p(-x) is equal to

Detailed Solution for Test: Polynomials - 1 - Question 25

 p(x)=x+3

 p(-x)=-x+3

p(x)+p(-x)=x+3-x+3=6

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