Question Text
Question 1 :
The length of a rectangular verandah is $3\:m$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking $x$ as the breadth of the verandah, write an equation in $x$ that represents the above statement.
Question 2 :
Is the following equation quadratic?$\displaystyle -\frac{5}{3}\, x^{2}\, =\, 2x\, +\, 9$
Question 5 :
If roots of the equation $12x^2 + mx + 5 = 0$ are in the ratio $3 : 2$, then $m =$
Question 6 :
The roots of the equation $(b+c)x^2-(a+b+c)x+a=0$ $(a,b,c\ \epsilon \Q, b+c \neq a)$ are
Question 7 :
Find all values of parameter $a$ for which the quadratic equation $ \left( a+1 \right) { x }^{ 2 }+2\left( a+1 \right) x+a-2=0 $has two distinct roots.<br><br>
Question 8 :
Let $p,q\in \left\{ 1,2,3,4 \right\} $. The number of equations of the form $p{ x }^{ 2 }+qx+1=0$ having real roots is
Question 9 :
The number of values of $\displaystyle k$for which$\displaystyle \left ( x^{2} - \left ( k - 2 \right )x + k^{2} \right ) \left ( x^{2} + kx + \left ( 2k - 1 \right ) \right )$is a perfect square