Coefficients of a Polynomial

Q.

If $\frac{2x+3}{\left(x+1\right)(x-3)}=\frac{a}{x+1}+\frac{b}{x-3}$, then $a+b=$

1. $1$

2. $2$

3. $\frac{9}{4}$

4. None of these

Q. If the sum of the coefficients of the polynomial $a{x}^2+3x+5$ is zero, what is the value of a ?

1. -3
2. 5
3. 3
4. -8

Q. The coefficient of a term in a polynomial can be any real number.

1. False
2. True

Q. Question 2 (iv)
Are the following statements ‘True’ or False’? Justify your answer.
iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Q. Consider the polynomial:

$a_n{x}^n$ + $a_{n-1}{x}^{n-1}$ + $a_{n-2}{x}^{n-2}$ + ....+$a_{1}x$ + $a_0$

When will this polynomial be called Zero Polynomial?

1. $a_n=0$
2. $a_n=a_{n-1}=....a_1=0$
3. $a_n=a_{n-1}=....a_1=a_0=0$
4. $a_0=0$

Q. What is the sum of the coefficients of $x^2$ in the polynomials

$p\left(x\right)=x^2+2x+1$
$q\left(x\right)=3x^2+4x+2$ ?

1. 3
2. 4
3. 5
4. 6

Q. Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.
$\frac{1}{4},-1$

Q. Find the quadratic polynomial where sum and product of the zeros are $a$ and $\frac{1}{a}$.

1. $a{x}^2+a^{2}x+1=0$
2. $a{x}^2-a^{2}x+1=0$
3. $a{x}^2-a^{2}x-1=0$
4. $a{x}^2-ax+1=0$

Q. What is the sum of the coefficents of $x$ in the polynomials $p\left(x\right)=3x+9$ and $q\left(x\right)=5x+8?$

1. 9
2. 25
3. 17
4. 8

Q. A term of any polynomial is a product of variables and a ___.

1. constant

2. another variable
3. zero
4. None of the above

Q. Zero polynomial can be written as ...................

1. $p\left(x\right)=0$
2. $p\left(x\right)=x^0$
3. $p\left(x\right)=x^1$
4. $p\left(x\right)=x^2$

Q.

What is the coefficient of $x^2$ in the polynomial $5x^3-4x^2+3x+10$ ?

1. 5

2. -4

3. 3

4. 10

Q. The zero of the polynomial $x^3-27$ is $3$

1. True
2. False