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Test: Polynomials Basics - Class 10 MCQ


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15 Questions MCQ Test The Complete SAT Course - Test: Polynomials Basics

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

A quadratic polynomial can have at most __________ terms.

Detailed Solution for Test: Polynomials Basics - Question 1

A polynomial of degree 2 is called quadratic polynomial.
Quadratic polynomials are of the form ax+ bx + c and it can contain at most three terms namely ax2, bx and c. Thus, we can say that a quadratic polynomial can have at most three terms.
Similarly, a polynomial of degree 1 is called linear polynomial and a polynomial of degree 3 is called cubic polynomial.

Test: Polynomials Basics - Question 2

If a quadratic polynomial's discriminant, D, is greater than zero, the polynomial has

Detailed Solution for Test: Polynomials Basics - Question 2

If the discriminant of a quadratic polynomial, D > 0, then the polynomial has two real and unequal roots.

Test: Polynomials Basics - Question 3

What is the degree of 0?

Detailed Solution for Test: Polynomials Basics - Question 3

Degree of the zero polynomial is not defined.
Zero polynomial is denoted by 0, and degree for that is not defined.

Test: Polynomials Basics - Question 4

The quadratic polynomial whose zeroes are 3 + √2 and 3 – √2 is

Detailed Solution for Test: Polynomials Basics - Question 4

S is the sum of zeroes and P is the product of zeroes: 

S = (3 + √2) + (3 – √2) = 6

P = (3 + √2) x (3 – √2) = (3)2 – (√2)2 = 9 – 2 = 7

So, Quadratic polynomial = x2 – Sx + P = x2 – 6x + 7

Test: Polynomials Basics - Question 5

What is the degree of a polynomial 7?

Detailed Solution for Test: Polynomials Basics - Question 5

Degree of a non-zero constant polynomial is zero.
We can see that given polynomial 7 contain only one term and that is constant. 7 can also be written as 7x0.
Hence degree of 7 is zero.

Test: Polynomials Basics - Question 6

Zeros of p(x) = x2 - 27 are

Detailed Solution for Test: Polynomials Basics - Question 6

x2 - 27 = 0

x2 = 27

x = √27

x = ±3√3

Test: Polynomials Basics - Question 7

What is the degree of a polynomial of 4x+ 9x+ 5x+ 11?

Detailed Solution for Test: Polynomials Basics - Question 7

Degree of a polynomial is the highest power of variable in a polynomial.
The term with the highest power of x is 4x7 and exponent of x in that term is 7, so the degree of polynomial of 4x+ 9x+ 5x+ 11 is 7.

Test: Polynomials Basics - Question 8

If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial is

Detailed Solution for Test: Polynomials Basics - Question 8

Quadratic polynomial is x2 – Sx + P = 0, where S is the sum and P is the product

⇒ x2 – (-6)x + 5 = 0

⇒ x2 + 6x + 5 = 0

Test: Polynomials Basics - Question 9

What is the coefficient of x3 in a polynomial 6x4 + 3x2 + 8x + 5?

Detailed Solution for Test: Polynomials Basics - Question 9

Coefficient is the number which is multiplied with respective variable.
In the given polynomial 6x4 + 3x2 + 8x + 5, there is not an expression containing x3. So we can write 6x+ 3x+ 8x + 5 as 6x4 + 0x3 + 3x2 + 8x + 5. We can see that 0 is multiplied with expression x3, so coefficient of x3 is 0.

Test: Polynomials Basics - Question 10

 is a polynomial.

Detailed Solution for Test: Polynomials Basics - Question 10

For an expression to be a polynomial, exponent of variable has to be whole number.
 can be written as x-1/2. We can see that exponent of x is -1/2 which is not whole number (W = {0, 1, 2, 3…}). Hence, 1x√2 is not a polynomial.

Test: Polynomials Basics - Question 11

A polynomial of degree p has

Detailed Solution for Test: Polynomials Basics - Question 11

A polynomial's maximum number of zeroes equals the polynomial's degree.

Test: Polynomials Basics - Question 12

A polynomial's zeros can be represented graphically. The number of polynomial zeros equals the number of points on the graph of the polynomial

Detailed Solution for Test: Polynomials Basics - Question 12

The number of zeroes of a polynomial is equal to the number of points where the graph of polynomial intersects the x-axis.

Test: Polynomials Basics - Question 13

If p(x) is a polynomial of degree one and p(y) = 0, then y is said to be

Detailed Solution for Test: Polynomials Basics - Question 13

Let p(x) = mx + n

Put x = y

p(y) = my + n = 0

So, y is zero of p(x).

Test: Polynomials Basics - Question 14

The degree of the polynomial, x5 – 2x2 + 2 is

Detailed Solution for Test: Polynomials Basics - Question 14

In every polynomial, the highest power of the variable is called a degree.

Test: Polynomials Basics - Question 15

If the zeroes of the quadratic polynomial ay2 + by + c, c ≠ 0 are equal, then

Detailed Solution for Test: Polynomials Basics - Question 15

Discriminant will be equal to zero for equal roots:

b2 - 4ac = 0

b2 = 4ac

ac = b2/4

ac > 0 (square of any number cannot be negative)

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