Polynomials Test

Result

Polynomials Test - 43

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Weekly Quiz Competition

Question 1
1 / -0

Find the degree of the given algebraic expression $$ax^2+bx+c$$.

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

We know that the degree is the term with the greatest exponent.

Since the highest exponent is $$2$$, therefore, the degree of $$ax^2+bx+c$$ is $$2$$.

Hence, the degree of the algebraic expression $$ax^2+bx+c$$ is $$2$$.
Question 2
1 / -0

What is the degree of the given monomial $$7y$$?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$7$$

Solution

We know that the degree is the term with the greatest exponent and,
To find the degree of a monomial with more than one variable for the same term, just add the exponents for each variable to get the degree.

Here, the given monomial $$7y$$ has one variable $$y$$ where the power of $$y$$ is $$1$$. Therefore degree of the monomial $$7y$$ is:

$$1$$ (The exponent of the variable)

Hence, the degree of the monomial $$7y$$ is $$1$$.
Question 3
1 / -0

Degree of the polynomial $$13 + 11x + 12x^3 + 3x^2$$ is

A
$$2$$

B
$$1$$

C
$$3$$

D
$$4$$

Solution

The degree of an individual term of a polynomial is the exponent of its variable
$$13+11x+12{x}^{3}+3{x}^{2}=12{x}^{3}+3{x}^{2}+11x+13$$
The highest exponent of $$x$$ is $$3$$
$$\therefore\,$$ Degree$$ =3$$
Question 4
1 / -0

The graph of the polynomial $$P(x) = ax-b$$, where $$a \neq 0; a, b \epsilon R$$ intersects X-axis in ...............point.

A
$$(0, \dfrac{b}{a})$$

B
$$(-\dfrac{b}{a}, 0)$$

C
$$(\dfrac{b}{a}, 0)$$

D
$$(-\dfrac{a}{b}, 0)$$

Solution
Question 5
1 / -0

If $$f\left( x \right) =2{ x }^{ 4 }-13{ x }^{ 2 }+ax+b$$ is divisible by $${ x }^{ 2 }-3x+2$$, then $$(b,a)=?$$

A
$$(-9,-2)$$

B
$$(6,4)$$

C
$$(2,9)$$

D
$$(7,-4)$$

Solution
Question 6
1 / -0

The graph of linear polynomial $$p(x)=3x-6$$ intersects the $$x-$$axis at________

A
$$(0,6)$$

B
$$(3,-6)$$

C
$$(0,2)$$

D
$$(2,0)$$

Solution
Question 7
1 / -0

The degree of the polynomial $$\frac { 4 }{ 5 } { x }^{ 2 }-\frac { 7 }{ 5 } x+\frac { 2 }{ 3 } { x }^{ 3 }+6$$ is :

A
2

B
1

C
3

D
0

Solution
Question 8
1 / -0

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

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

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

C
$$\dfrac{2}{3}$$

D
$$\dfrac{-2}{3}$$

Solution

Given $$-3$$ is the zero of the polynomial $$(k-1)x^2+ k x+1$$
So $$-3$$ must satisfy the equation $$(k-1)x^2+k x+1=0$$
$$\implies (k-1)(-3)^2+k(-3)+1=0$$
$$\implies 9(k-1)-3 k+1=0$$
$$\implies 9 k-9-3 k+1=0$$
$$\implies 6 k=8$$
$$\implies k=\dfrac{4}{3}$$
Question 9
1 / -0

Which of the following graph represents linear polynomial.

A

B

C

D

Solution
Question 10
1 / -0

Which one of the following is the second degree polynomial function $$f(x)$$ where $$f(0)=5,f(-1)=10$$ and $$f(1)=6\,?$$

A
$$5x^2-2x+5$$

B
$$3x^2-2x-5$$

C
$$3x^2-2x+5$$

D
$$3x^2-10x+5$$

Solution

here we use, trial and error method,

Given,

$$f(0)=5,f(-1)=10,f(1)=6$$

check for $$x=0$$, for which option we get, $$f(0)=5$$

we have, options A,C,D

now check for, $$x=1$$ for which option we get, $$f(1)=6$$

we have, option C

$$3x^2-2x+5$$