Question 4 :
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 5 :
If the roots of $${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$$ lie between $$-2$$ and $$4$$, then
Question 6 :
Is $$(3x^{2} + 5xy + 4y^{2})$$ a factor of $$ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$$?<br/>
Question 7 :
Simplify:Find$$\ x(x + 1) (x + 2) (x + 3) \div  x(x + 1)$$<br/>
Question 8 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$$49x^2-81$$<br/>
Question 9 :
State whether True or False.Divide : $$a^2 +7a + 12 $$ by $$  a + 4 $$, then the answer is $$a+3$$.<br/>
Question 10 :
If $$\alpha , \beta$$ are the roots of equation $$x^2 \, - \, px \, + \, q \, = \, 0,$$ then find the equation the roots of which are $$\left ( \alpha ^2  \, \beta ^2 \right )  \,  and  \,  \,  \alpha \, + \,\beta $$.
Question 11 :
$$\alpha $$ 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 13 :
Work out the following divisions.$$10y(6y + 21) \div 5(2y + 7)$$<br/>
Question 14 :
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 15 :
Factorise the expressions and divide them as directed.$$4yz(z^2 + 6z-  16)\div  2y(z + 8)$$<br/>
Question 17 :
What is $$\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$$ equal to
Question 18 :
Find the value of a & b, if  $$8{x^4} + 14{x^3} - 2{x^2} + ax + b$$ is divisible by $$4{x^2} + 3x - 2$$
Question 21 :
The remainder when$$4{a^3} - 12{a^2} + 14a - 3$$ is divided by $$2a-1$$, is
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 25 :
If $$\alpha , \beta$$ are the zeros of the polynomials $$f(x) = x^2+x+1 $$ then $$\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$$________.
Question 26 :
Find the expression which is equivalent to : $$\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $$?
Question 28 :
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 29 :
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 30 :
If a polynomial $$p(x)$$ is divided by $$x - a$$ then remainder is<br/>
Question 31 :
State whether True or False.Divide: $$12x^2 + 7xy -12y^2 $$ by $$ 3x + 4y $$, then the answer is $$x^4+2x^2+4$$.<br/>
Question 32 :
If $$P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$$ and $$Q=\dfrac {x+6}{x+7}$$ then the value of $$\dfrac {P}{Q}$$ is:
Question 34 :
What is the remainder, when<br>$$(4{x^3} - 3{x^2} + 2x - 1)$$ is divided by (x+2)?<br>
Question 38 :
Factorise the expressions and divide them as directed.$$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$$
Question 39 :
If $$a\ne 2$$, which of the following is equal to $$\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $$?
