Question 1 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$$a^2-b^2 ; a-b$$
Question 2 :
If the roots of $${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$$ lie between $$-2$$ and $$4$$, then
Question 3 :
Factorise the expressions and divide them as directed.$$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$$
Question 4 :
$$\alpha $$ 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 5 :
State whether true or false:Divide: $$4a^2 + 12ab + 91b^2 -25c^2 $$ by $$ 2a + 3b + 5c $$, then the answer is $$2a+3b+5c$$.<br/>
Question 6 :
If $$\alpha , \beta $$ are the roots of the equation $$ax^{2}+bx+c=0$$, find the value of $$\alpha ^{2}+\beta ^{2}$$.
Question 7 :
State whether the following statement is true or false.After dividing $$ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$$ by $$ (3x^{2}+5xy + 4y^{2})$$ we get<br/>$$3x^{2}-4xy + 8y^{2}$$
Question 9 :
Choose the correct answer from the alternatives given.<br>If the expression $$2x^2$$ + 14x - 15 is divided by (x - 4). then the remainder is
Question 11 :
The condition that one root is twice the other root of the quadratic equation$$\displaystyle x^{2}+px+q=0$$ is
Question 12 :
The sum of the reciprocals of the roots of the equation$$\displaystyle \frac{2009}{2010}x+1+\frac{1}{x}=0$$ is
Question 13 :
If $$p$$ and $$q$$ are the roots of the equation $$ax^2 +bx +c =0$$, then the value of $$\dfrac {p}{q}+\dfrac {q}{p}$$ is<br/>
Question 15 :
If $$x^4 \, + \, 2x^3 \, - \, 3x^2 \, + \, x \, - \, 1$$ is divided by $$x - 2$$. then the remainder is
Question 16 :
If the sum of two numbers is $$9$$ and the sum of their squares is $$41$$, then the numbers are<br/>
Question 19 :
If $$\alpha$$ and $$\beta$$ are the zeros of the polynomial $$f(x)=6x^2-3-7x$$, then $$(\alpha+1)(\beta+1)$$ is equal to<br/>
Question 20 :
The sum and product of zeros of the quadratic polynomial are - 5 and 3 respectively the quadratic polynomial is equal to<br>
Question 21 :
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 22 :
<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>
Question 23 :
When $${ x }^{ 2 }-2x+k$$ divided the polynomial $${ x }^{ 2 }-{ 6x }^{ 3 }+16{ x }^{ 2 }-25x+10$$ the reminder is (x+a), the value of is
Question 24 :
The area of a rectangle is $$\displaystyle 12y^{4}+28y^{3}-5y^{2}$$. If its length is $$\displaystyle 6y^{3}-y^{2}$$, then its width is
Question 26 :
State the following statement is True or False<br/>The zeros of the polynomial $$(x - 2) (x^{2} + 4x + 3)$$ are $$2,-1 and -3$$
Question 27 :
If $$\alpha, \beta$$ be the roots $$x^2+px-q=0$$ and $$\gamma, \delta$$ be the roots of $$x^2+px+r=0$$, then $$\dfrac{(\alpha -\gamma)(\alpha -\delta)}{(\beta -\gamma )(\beta -\delta)}=$$
Question 29 :
The number of integers $$n$$ for which $$3x^3-25x+n=0$$ has three real roots is$$?$$<br/>
Question 30 :
Let $$\alpha$$ and $$\beta$$ be the roots of equation $$x^2-6x-2=0$$. If $$a_n=\alpha^n-\beta^n$$, for $$n\geq 1$$, then the value of $$\dfrac{a_{10}-2a_8}{2a_9}$$ is equal to?