Question 1 :
If one zero of $2x^2-3x + k$ is reciprocal to the other, then the value of k is
Question 3 :
The zero of the polynomial $p(x) = 2x + 5$ is :<br>
Question 7 :
Verify whether the following are zeros of the polynomial indicated against them:<br/>$s(x)=x^2, \ x=0, 1$<br/>
Question 8 :
Factorise the expressions and divide them as directed.$39y^3(50y^2 -98) \div 26y^2(5y + 7)$
Question 12 :
The remainder when $x^{6} - 3x^{5} + 2x^{2} + 8$ is divided by $x - 3$ is<br>
Question 13 :
Simplify:$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/>
Question 14 :
Verify whether the following are the zeros of the polynomial indicated against them:$p(x)=(x-2)(x-5), \  x=2, 5$<br/>
Question 15 :
State whether the statement is True or False.Evaluate: $(4x^2-5y^2)(4x^2+5y^2)$ is equal to $16x^4-25y^4$.<br/>
Question 16 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of  $\displaystyle x - \dfrac{1}{x}$
Question 17 :
Choose the correct answer from the alternatives given.<br/>If x - $\dfrac{1}{x}$ = 3 then find the value of $x^3 + \dfrac{1}{x^3}$. 
Question 18 :
One factor of $x^4 + x^2-20$ is $x^2+ 5$. The other factor is
Question 19 :
Which of the following polynomials has $- 3$ as a zero ?<br>
Question 20 :
If (x -1) is a factor of polynomial f(x) but not of g(x), then it must be a factor of
Question 21 :
State whether True or False, if the following are zeros of the polynomial, indicated against them:$p(x)=lx+m, \ x=-\dfrac {m}{l}$<br/>
Question 22 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in each of the following cases:$p(x)=2x^2+kx+\sqrt 2$<br/>
Question 23 :
If $\left (x + \dfrac {1}{x}\right ) = 2\sqrt {3}$, then the value of $\left (x^{3} + \dfrac {1}{x^{3}}\right )$ is
Question 24 :
Let $r(x)$ be the remainder when the polynomial $x^{135}+x^{126}-x^{115}+x^{5}+1$ is divided by $x^{3}-x$. Then:
Question 26 :
Find the remainder when $x^{3} + 3x^{2} + 3x + 1$ is divided by $x - \dfrac {1}{2}$.
Question 27 :
If $\dfrac{a}{b}$ + $\dfrac{b}{a}$ = 1, then $a^3$ + $b^3$ $=$
Question 28 :
If $f\left( x \right) = {\left( {\dfrac{3}{5}} \right)^x} + {\left( {\dfrac{4}{5}} \right)^x} - 1,x \in R$, then the equation $f(x) = 0$ has :
Question 29 :
The value of $k$ for which $x - k$ is a factor of $x^{3} - kx^{2} + 2x + k + 4$ is<br/>
Question 30 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in the following cases:$p(x)=kx^2-\sqrt 2x+1$<br/>
Question 31 :
$x+ \dfrac{1}{x}= 2$ , x $\neq $ 0.then value of $x^2 + \dfrac{1}{x^2}$ is equal to
Question 32 :
State whether the statement is True or False.Evaluate: $(6-xy)(6+xy)$ is equal to $36-x^2y^2$.<br/>
Question 33 :
Find the value of 'a' if (x-2) is factor of $2x^3-6x^2+5x+a$.
Question 34 :
If the polynomial $3x^4-4x^3-3x-1$ is divided by $x-1$, then the remainder is :
Question 35 :
If one of zeroes of the cubic polynomial ${x^3} + a{x^2} + bx + c\,\,\,$ is -1 , then the product of the other two zeroes is <br/>
Question 37 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$<br/>
Question 40 :
If $\displaystyle a + \dfrac{1}{a} = m$ and $\displaystyle a \neq 0$; find in terms of $\displaystyle 'm'$ ; the value of: $\displaystyle a - \dfrac{1}{a}$
Question 41 :
If ${ x }^{ 3 }+ax-28$ is exactly divisible by $x-4$, then the value of $a$ is
Question 43 :
State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.<br/>
Question 44 :
<b></b>If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a+b $. 
Question 45 :
A polynomial of degree $n$ can have at most $n$ zeros.<br/>
Question 46 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>
Question 48 :
If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x) = 2x^{2} -7x +3$, find the value $\alpha^{2} + \beta^{2}$.