Question 1 :
Find the value of $k$ for the following quadratic equation, so that they have two real and equal roots:$x^2 - 2(k + 1)x + k^2 = 0$
Question 2 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 3 :
If the roots of the equation $\displaystyle x^{2}+px-6=0$ are $6$ and $-1$ then the value of $p$ is
Question 4 :
If $\alpha, \beta$ are the roots of the equation $2x^2 + 4x-5=0$, the equation whose roots are the reciprocals of $2\alpha -3$ and $2 \beta -3$ is<br>
Question 5 :
If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has _______ roots.<br/>
Question 6 :
Find the value of K so that sum of the roots of the equations $3x^2 + (2x - 11) x K - 5 = 0$ is equal to the product of the roots.
Question 7 :
If the roots of the equation $\displaystyle \left ( a^{2}+b^{2} \right )x^{2}-2b\left ( a+c \right )x+\left ( b^{2}+c^{2} \right )=0 $ are equal then
Question 8 :
If one of roots of $x^2+ ax + 4 = 0$ is twice the other root, then the value of 'a' is .
Question 9 :
If the roots of the equation $a{ x }^{ 2 }+bx+c=0$ are reciprocal of each other, then
Question 10 :
If $a, b, c \in  Q, $ then roots of $ax^2 + 2(a + b)x (3a + 2b) = 0$ are<br/>
Question 11 :
If $x_1$ and $x_2$ are the roots of $3x^2 - 2x - 6 = 0$, then $x_1^2 + x_2^2$ is equal to
Question 12 :
The roots of the following quadratic equation are not real<br/>$2x^2- 3x + 5$ = 0
Question 13 :
The given quadratic equations have real roots and roots are $\dfrac{\sqrt5}{3}, \, -\sqrt5$ :<br/> $3x^2 \, + \, 2\sqrt{5x} \, - \, 5 \, = \, 0$
Question 14 :
If the roots of the equation $ x^{2} -15-m(2x-8)=0 $ are equal, then $m =$
Question 15 :
If roots of the equation $x^2-bx+c=0$ be two consecutive integers, then $b^2-4c$ equals :
Question 16 :
If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by atmost $4$ then the least value of $b$ is-
Question 17 :
Determine the value of $k$ for which the $x = -a$ is a solution of the equation $\displaystyle x^{2}-2\left ( a+b \right )x+3k=0 $<br/>
Question 18 :
Say true or false:The following equation has real roots$\cfrac{1}{2x-3}-\cfrac{1}{x-5}=1,   x \neq \{\cfrac{3}{2},5\}$<br/>
Question 19 :
The values of k for which the roots are real and equal of the following equation<br/>$4x^2$ - 3kx + 1 = 0 are $k = \pm \dfrac{4}{3}$<br/>
Question 20 :
The value of k for which the equation $x^{2} - 4x + k = 0 $ has equal roots is<br/>
Question 21 :
The difference between two positive integers is $13$ and their product is $140$. Find the two integers.<br/>
Question 22 :
A tradesman finds that by selling a bicycle for Rs. 75, which he had bought for Rs. $x$, he gained $x$%. Find the value of $x$.
Question 23 :
If $\alpha$, $\beta$ are the roots of the equation $a{ x }^{ 2 }+bx+x=0$, then the roots of the equation $\left( a+b+c \right) { x }^{ 2 }-\left( b+2c \right) x+c=0$ are
Question 24 :
If $\alpha, \beta$ are the roots of the equation $2x^{2} - 3x - 6 = 0$, then the equation whose roots are $\alpha^{2} + 2$ and $\beta^{2} + 2$ is
