Question 1 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 2 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
Question 3 :
If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.
Question 4 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.<br/>
Question 7 :
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 10 :
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 11 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$
Question 12 :
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 13 :
Divide the following and write your answer in lowest terms: $\dfrac{2x^2+5x-3}{2x^2+9x+9}\div \dfrac{2x^2+x-1}{2x^2+x-3}$
Question 14 :
If the roots of the equation $x^2 + 2bx + c = 0$ are $\alpha$ and $\beta$, then $b^2 - c$ is equal to
Question 15 :
$mx^2+(m-1)x +2=0$ has roots on either side of x=1 the m $\in$
Question 16 :
$\alpha $ and $\beta $ are the roots of ${ x }^{ 2 }+2x+C=0$. If ${ \alpha  }^{ 3 }+{ \beta  }^{ 3 }=4$, then the value of $C$ is
Question 17 :
If $a, b$ are the roots of $x^2 + px + 1 = 0$ and $c, d$ are the roots of $x^2 + qx + 1 = 0,$ the value of $E = (a - c)(b - c)(a + d) ( b + d)$ is
Question 18 :
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 19 :
The difference of the roots of$\displaystyle 2y^{2}-ky+16=0$ is 1/3 Find k
