Polynomials Test

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Polynomials Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

The zeroes of the polynomial $$p(x)=(x-6) (x-5)$$ are :

A
$$-6, -5$$

B
$$-6, 5$$

C
$$6, -5$$

D
$$6, 5$$

Solution

To find the zeroes of the polynomial means to find those values of x for which the value of equation is zero.
$$p(x)=0$$.
$$p(x)=\left( x-6 \right) \left( x-5 \right) $$=0
hence $$x-6=0 , x=6$$ OR $$x-5=0,x=5$$.
Therefore, option $$D$$ is correct.
Question 2
1 / -0

A cubic polynomial is a polynomial with degree :

A
1

B
3

C
0

D
2

Solution

A cubic polynomial is a polynomial of degree 3, or in simplier terms highest power of x is 3,
It of the form $$f(x)=a{ x }^{ 3 }+b{ x }^{ 2 }+cx+d$$ where a,b,c,d belongs to real numbers.
Hence correct option is B.
Question 3
1 / -0

If the degree of polynomial $$p(x)$$ is $$a$$, then the number of zeroes of $$p(x)$$ would be :

A
$$a+1$$

B
$$a-1$$

C
$$a$$

D
$$2a$$

Solution

For a polynomial of degree $$a$$, the number of roots (zeros) is $$a$$.
Let a general polynomial of degree $$n$$ be
$$ p(x)= a^{}_{n}x^n+a{}_{n-1}x^{n-1}+........+a{}_{0}$$
Here, this polynomial has $$n$$ roots (zeros), which can be real, imaginary or both depending on the polynomial.
That is, a polynomial of degree $$a$$ has $$a$$ zeroes.

Therefore, option $$C$$ is correct.
Question 4
1 / -0

Zero of the polynomial $$3 \pi x-4$$ is :

A
$$\dfrac{4}{3\pi}$$

B
$$\dfrac{3\pi}{4}$$

C
$$\dfrac{4\pi}{3}$$

D
$$0$$

Solution

Zero of a polynomial is the value of the variable for which the polynomial becomes $$zero$$.
So, for $$3\pi x-4=0$$
$$\implies$$ $$x=\dfrac {4}{3\pi}$$, is the required zero.
Hence, $$A$$ is correct.
Question 5
1 / -0

A quadratic polynomial can have at most $$2$$ zeroes and a cubic polynomial can have at most ........ zeroes.

A
$$3$$

B
$$2$$

C
$$1$$

D
None of the above

Solution

'The maximum number of possible roots (zeros) of a polynomial is equal to its degree, so cubic polynomial has at most 3 roots (zeros).
Therefore, option $$A$$ is correct.
Question 6
1 / -0

The degree of the polynomial $$2 - y^{2} - y^{3} + 2y^{7}$$ is :

A
2

B
7

C
0

D
3

Solution

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Hence, for $$2-y^2-y^3+2y^7$$, the degree$$=7$$
So, answer is $$B$$.
Question 7
1 / -0

Use the identity $$ (a+b)(a-b) = a^2-b^2$$ to evaluate:
$$21\times 19 $$.

A
$$389$$

B
$$399$$

C
$$289$$

D
$$429$$

Solution

We know, $$ 21 \times 19 = (20+ 1) \times (20 - 1) $$ .

Applying the formula $$ (a+b)(a-b) = { a }^{ 2 }-{ b }^{ 2 } $$, where $$ a = 20 , b = 1 $$,
we get,
$$ 21 \times 19 = (20+ 1) \times (20 - 1) = { 20 }^{ 2 }-{ 1 }^{ 2 } = 400 - 1 = 399 $$ .
Therefore, option $$B$$ is correct.
Question 8
1 / -0

What is the degree of the following polynomial expression:
$$\dfrac{4}{3}x^{7} - 3x^{5} + 2x^{3} + 1$$

A
7

B
4

C
5

D
3

Solution

Clearly, the degree of the polynomial expression $$\dfrac{4}{3}x^{7} - 3x^{5} + 2x^{3} + 1$$ is $$7$$.
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Question 9
1 / -0

Find the degree of the following polynomial
$$x^9-x^4+x^{12}+x-2$$

A
12

B
9

C
4

D
2

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$x^9-x^4+x^{12}+x-2$$
Since there are 4 terms $$x^9-x^4+x^{12}+x-2$$, this is a polynomial and has the highest degree $$x^{12}$$ of all the terms.
Therefore,
Degree is $$12$$
Question 10
1 / -0

Find the degree of the following polynomial
$$3y+4y^2$$

A
y

B
0

C
1

D
2

Solution

We know that, the degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given polynomial is $$3y+4y^2$$
It is a polynomial in $$y$$ having highest exponent value as $$2$$.

Hence, the degree of the given polynomial is $$2$$.

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Polynomials Test - 18

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Polynomials Test - 18

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Question 1

$$-6, -5$$

$$-6, 5$$

$$6, -5$$

$$6, 5$$

Solution

Question 2

1

3

0

2

Solution

Question 3

$$a+1$$

$$a-1$$

$$a$$

$$2a$$

Solution

Question 4

$$\dfrac{4}{3\pi}$$

$$\dfrac{3\pi}{4}$$

$$\dfrac{4\pi}{3}$$

$$0$$

Solution

Question 5

$$3$$

$$2$$

$$1$$

None of the above

Solution

Question 6

2

7

0

3

Solution

Question 7

$$389$$

$$399$$

$$289$$

$$429$$

Solution

Question 8

7

4

5

3

Solution

Question 9

12

9

4

2

Solution

Question 10

y

0

1

2

Solution

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