Question 1 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then $y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>
Question 2 :
Check whether $2x^2 - 3x + 5 = 0$ has real roots or no.<br/>
Question 3 :
A quadratic equation $ax^2 + bx+c=0$ has two distinct real roots, if<br>
Question 4 :
Is the following equation quadratic?$(x\, +\, 3) (x\, -\, 4)\, =\, 0$
Question 5 :
In a rectangle the breadth is one unit less than the length and the area is $12$ sq.units. Find the length of the rectangle.
Question 6 :
The mentioned equation is in which form?$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$
Question 7 :
State the following statement is True or False<br/>The digit at ten's place of a two digit number exceeds the square of digit at units place ($x$) by 5 and the number formed is $61$, then the equation is $10\, (x^{2}\, +\, 5)\, +\, x\, =\, 61$.<br/>
Question 8 :
Solve for $x : 15 x^2 - 7x - 36 = 0$<br>
Question 9 :
State the following statement is True or False<br/>The sum of a natural number $x$ and its reciprocal is $\displaystyle \frac{37}{6}$, then the equation is $x\, +\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{37}{6}$.<br/>
Question 11 :
Equation of the tangent at (4 , 4) on $x^2$ = 4y is
Question 12 :
Find c, if the quadratic equation $x^{2}\, -\, 2\, (c\, +\, 1)\, x\, +\,  c^{2}\, =\, 0 $ has real and equal roots. <br/>
Question 13 :
If in applying the quardratic formula to a quadratic equation<br>$f(x) = ax^2 + bx + c = 0$, it happens that $c = b^2/4a$, then the graph of $y = f(x)$ will certainly:
Question 15 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 16 :
Determine the nature of roots of the given equation from its discriminant.<br/>$x^{2}\, +\, 3\sqrt2x\, -\, 8\, =\, 0$
Question 17 :
If the equation $\displaystyle \lambda x^{2}-2x+3= 0$has positive roots for some real$\displaystyle \lambda $, then
Question 18 :
Assertion: If $a$ and $b$ are integers and the roots of $x^2+ax+b=0$ are rational then they must be integers.
Reason: If the coefficient of $x^2$ in a quadratic equation is unity then its roots must be integers.
Question 19 :
The set of values of k for which the given quadratic equation has real roots<br/>$2x^2$ + kx +2 = 0 is k $\leq$ 9
Question 20 :
If the roots of the equation $\displaystyle x^{2}+px-6=0$ are $6$ and $-1$ then the value of $p$ is
Question 21 :
If both the roots of the equation ${ x }^{ 2 }-32x+c=0$ are prime numbers then the possible values of $c$ are
Question 22 :
Consider the quadratic equation $(1+m)x^2-2(1+3m)x+(1+8m)=0$, (where $m \in R-\left \{-1\right \})$, then the set of values of $'m'$ such that the given quadratic equation has both roots positive are,
Question 23 :
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
Question 24 :
If $\alpha \,\& \beta $ are  roots if the equation ${x^2} + 5x - 5 = 0$, then evaluate $\dfrac{1}{{{{(\alpha  + 1)}^3}}} + \dfrac{1}{{{{(\beta  + 1)}^3}}}$
Question 25 :
All the values of '$a$' for which the quadratic expression $ax^2+(a-2)x-2$ is negative for exactly two integral values of $x$ may lie in