Question 1 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>
Question 2 :
A polynomial of the form $ax^5 + bx^3 + cx^2 + dx + e$ has almost ________ zeroes.
Question 3 :
If $\alpha$ and $\beta$ are the zeroes of the polynomial $ 5x^{2}-7x+2$, then, the sum of their reciprocals is :<br/>
Question 4 : <span>Find the Quotient and the Remainder when the first polynomial is divided by the second.</span><div>$-6x^4 + 5x^2 + 111$ by $2x^2+1$</div>
Question 5 :
$ax^3 + bx^2 + cx + d = 0$ is said to be cubic polynomial if _________.
Question 7 :
What is the remainder when $\left( 2{ x }^{ 2 }+3x+7 \right) $ is divided by $\left( x+2 \right) $?
Question 10 : Simplify:<div>$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/></div>
Question 11 : <div><span>Find a quadratic polynomial whose sum and product respectively of the zeros, are </span><span>$\dfrac {-3}{2\sqrt 5}, -\dfrac {1}{2}$</span><span>.</span></div>
Question 13 :
If $\alpha $ and $\beta$ are the zeroes of the quadratic polynomial $4x^{2}+4x+1$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.
Question 14 :
On dividing p $(4p^{2} - 16)$ by $4p (p-2)$, we get<br>
Question 15 :
If $\alpha $ and $\beta $ are zeros of the polynomial $2x^2-4x +5$, find the values of:<br>$\alpha ^3+\beta^3$
Question 16 :
If $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }-5x+4=0$ then ${ \left( { \alpha }^{ 3 }+{ \beta }^{ 3 }+{ \gamma }^{ 3 } \right) }^{ 2 }=$
Question 17 :
The number of different possible values for the sum $x+y+z$, where $x,y,z$ are real numbers such that ${x}^{4}+4{y}^{4}+16{z}^{4}+64=32xyz$ is
Question 18 :
The number of integers $n$ for which $3x^3-25x+n=0$ has three real roots is$?$<br/>
Question 19 :
Suppose $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $ then $f(x)=$
Question 20 :
Number of intergers in the range of 'a' so that the equation ${ x }^{ 3 }-3x+a=0$ has all its roots real and distinct,is
