Question 2 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$$\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$$
Question 3 :
The degree of the remainder is always less than the degree of the divisor.
Question 4 :
If the roots of $${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$$ lie between $$-2$$ and $$4$$, then
Question 5 :
If $$\alpha , \beta $$ are the roots of the equation $$ax^{2}+bx+c=0$$, find the value of $$\alpha ^{2}+\beta ^{2}$$.
Question 6 :
State whether True or False.Divide: $$x^2 + 3x -54 $$ by $$ x-6 $$, then the answer is $$x+9$$.<br/>
Question 8 :
The remainder when$$4{a^3} - 12{a^2} + 14a - 3$$ is divided by $$2a-1$$, is
Question 10 :
What must be added to $$x^3-3x^2-12x + 19$$, so that the result is exactly divisible by $$x^2 + x-6$$?
Question 12 :
Work out the following divisions.$$10y(6y + 21) \div 5(2y + 7)$$<br/>
Question 14 :
If the quotient of $$\displaystyle x^4 - 11x^3 + 44x^2 - 76x +48$$. When divided by $$(x^2 - 7x +12)$$ is $$Ax^2 + Bx + C$$, then the descending order of A, B, C is
Question 15 :
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients.$$2s^2-(1+2\sqrt 2)s+\sqrt 2$$<br/>
Question 16 :
If $$a\ne 2$$, which of the following is equal to $$\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $$?
Question 17 :
$$\alpha $$ and $$\beta $$ are zeroes of polynomial $$x^{2}-2x+1,$$ then product of zeroes of a polynomial having zeroes $$\dfrac{1}{\alpha }$$  and    $$\dfrac{1}{\beta }$$ is
Question 19 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$$a^2-b^2 ; a-b$$
Question 20 :
If $$\alpha , \beta$$ are the zeros of the polynomials $$f(x) = x^2+x+1 $$ then $$\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$$________.
Question 22 :
If $$\alpha$$ and $$\beta$$ are the zeroes of the polynomial $$4x^{2} + 3x + 7$$, then $$\dfrac{1}{\alpha }+\dfrac{1}{\beta }$$ is equal to:<br/>
Question 24 :
Apply the division algorithm to find the remainder on dividing $$p(x) = x^4 -3x^2 + 4x + 5$$ by $$g(x)= x^2 +1 -x.$$
Question 26 :
Divide:$$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$$ by $$(3y-2)$$Answer: $$5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$$
Question 27 :
What is $$\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$$ equal to
Question 30 :
What must be subtracted from $$4x^4 - 2x^3 - 6x^2 + x - 5$$, so that the result is exactly divisible by $$2x^2 + x - 1$$?
Question 32 :
State whether True or False.Divide: $$16 + 8x + x^6-8x^3 -2x^4+ x2 $$ by $$ x+ 4-x^3$$, then the answer is $$-x^3+x+4$$.<br/>
Question 33 :
Find all values of a for which the equation $$x^4+(a−1)x^3+x^2+(a−1)x+1=0$$ possesses at least two distinct negative roots.
Question 34 :
There are $$x^{4} + 57x + 15$$ pens to be distributed in a class of $$x^{2} + 4x + 2$$ students. Each student should get the minimum possible number of pens. Find the number of pens received by each student and the number of pens left undistributed $$(x\epsilon N)$$.
Question 35 :
If $$\alpha, \beta$$ are the roots of the quadratic equation $$ax^2+bx+c=0$$ and $$3b^2=16ac$$ then
Question 36 :
For the equation $$3x^{2}+px+3=0,p < 0$$ if one of the roots is square of the other, then $$p$$ is eqal to:
Question 38 :
If $$\alpha$$ and $$\beta$$ be two zeros of the quadratic polynomial $$ax^2+bx+c$$, then evaluate:$$\alpha^3+\beta^3$$<br/>
Question 40 : <p>The simplified form of the expression given below is :-</p><p>$$\eqalign{& \underline {{y^4} - {x^4}} - \underline {{y^3}} \cr & \dfrac{{x\left( {x + y} \right)\;x}}{{{y^2} - xy + {x^2}}} \cr} $$</p>
