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Test: Introduction To Polynomials


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20 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Introduction To Polynomials

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

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

Test: Introduction To Polynomials - Question 2

A polynomial of degree ‘3’ is called

Test: Introduction To Polynomials - Question 3

Solution of a quadratic equation x²+ 5x - 6 = 0

Detailed Solution for Test: Introduction To Polynomials - Question 3

x²+ 5x - 6 = 0
x² - x + 6x - 6
x (x-1) + 6 (x-1)
(x-1) (x+6)
x = 1; x = -6

Test: Introduction To Polynomials - Question 4

If 3 + 5 – 8 = 0, then the value of (3)3 + (5)3 – (8)3 is

Detailed Solution for Test: Introduction To Polynomials - Question 4

3^3+5^3-8^3=27+125-512

=152-512

=-360

Test: Introduction To Polynomials - Question 5

Solution of a quadratic equation x²+ 5x - 6 = 0

Detailed Solution for Test: Introduction To Polynomials - Question 5

⇒ x²+ 5x - 6 = 0

⇒ x²+ 6x -x - 6 = 0

⇒ x(x+6) -1(x+6) = 0

⇒ (x-1) (x+6) = 0

⇒ x = 1, -6

 

Test: Introduction To Polynomials - Question 6

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

Detailed Solution for Test: Introduction To Polynomials - Question 6

use factor theorem as x+2 is factor of

x³-2ax²+16 so put x = -2 and equate the equation to 0

so putting x = -2

(-2)³-2a(-2)²+16 =0

-8-8a+16=0

-8a = -8

a = 8/8= 1

So,

a = 1

Test: Introduction To Polynomials - Question 7

Which of the following is not a quadratic polynomial?​

Test: Introduction To Polynomials - Question 8

P of x = ax, a is not equal to 0. find zeros of polynmial

Detailed Solution for Test: Introduction To Polynomials - Question 8

p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial. 
Checking:-
p(0) = a(0)
= 0

Test: Introduction To Polynomials - Question 9

Zero of the polynomial p(x) where p (x) = ax, a ≠ 0 is:

Test: Introduction To Polynomials - Question 10

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

Test: Introduction To Polynomials - Question 11

If p(x) = 7 – 3x + 2x2 then value of p(-2) is:

Detailed Solution for Test: Introduction To Polynomials - Question 11

p(-2) = 7 - 3(-2) + 2(-2)2

         = 7+6+8 = 21

Test: Introduction To Polynomials - Question 12

A linear polynomials has how many zeros

Detailed Solution for Test: Introduction To Polynomials - Question 12

A linear polynomial has 1 zero.

A quadratic polynomial has 2 zeroes.

A cubic polynomial has 3 zeroes.

In general, any polynomial has as many zeroes as its degree.

Test: Introduction To Polynomials - Question 13

If one of the factor of x2 + x – 20 is (x + 5). Find the other

Test: Introduction To Polynomials - Question 14

Which of the following is a quadratic polynomial in one variable?

Test: Introduction To Polynomials - Question 15

A cubic polynomial is a polynomial of degree …………

Detailed Solution for Test: Introduction To Polynomials - Question 15

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form 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: Introduction To Polynomials - Question 16

Find the value of the polynomial 6 – 4x + 3x2 at x = 3

Test: Introduction To Polynomials - Question 17

Degree of zero polynomial is:

Detailed Solution for Test: Introduction To Polynomials - Question 17

A zero polynomial is a polynomial in which all the coefficients are 0.

Let the polynomials highest power variable be x^n as per the above statement x^n = 0 

Now, The degree of the zero polynomial is log0 which is undefined. 

Hence. The degree of zero polynomial is undefined.

Test: Introduction To Polynomials - Question 18

Zero of a zero polynomial is:

Detailed Solution for Test: Introduction To Polynomials - Question 18

Zero of the zero polynomial is any real number.
e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number. 

Test: Introduction To Polynomials - Question 19

What is the coefficient of x in  x3 + 3x2 - 2x - 1

Test: Introduction To Polynomials - Question 20

The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is:

Detailed Solution for Test: Introduction To Polynomials - Question 20

The degree refers to the highest power of the polynomial. In this polynomial X has highest power 4.So the degree of polynomial is 4.

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