Question 2 :
The value of k for which the roots are real and equal of the following equation<br/>$x^2$ - 4kx + k = 0 are k = 0, $\dfrac{1}{4}$
Question 3 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 4 :
State the nature of the given quadratic equation $(x + 4)^2 + 8x = 0$
Question 5 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which, at least one root is greater than $2$.
Question 7 :
Equation of the tangent at (4 , 4) on $x^2$ = 4y is
Question 8 :
Find the values of $k$ for the following quadratic equation, so that they have two real and equal roots:$4x^2 - 2(k + 1)x + (k + 4) = 0$
Question 9 :
Determine the values of $p$ for which the quadratic equation $2x^2 + px + 8 = 0$ has real roots.
Question 10 :
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 11 :
If $\alpha$, $\beta$  are the roots of $3x^{2} - 4x + 1 = 0$ the equation whose roots are $\dfrac{\alpha}{\beta}, \dfrac{\beta}{\alpha}$ is?<br/>
Question 12 :
If difference of roots of the equation$\displaystyle x^{2}+px+8= 0$ is $2$, then $p$ is equal to
Question 14 :
I. lf one root of the equation $5x^{2}+13x+k=0$ is the reciprocal of the other, then $k=5$<br>II. lf the roots of the equation $a(b-c)x^{2}+b(c-a)x+c(a-b)=0$ are equal, then $a, b,c$ are in H.P.<br>Which of the above statement is true?<br>
Question 15 :
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 16 :
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 17 :
The given quadratic equations have real roots and roots are $\dfrac{\sqrt5}{3}, \, -\sqrt5$ :<br/> $3x^2 \, + \, 2\sqrt{5x} \, - \, 5 \, = \, 0$
Question 19 :
If ${x_1},{x_2}$ are the roots of ${x^2} - 3x + a = 0,a \in R$ and ${x_1} < 1 < {x_2}$ then $a$ belongs to: <br/>
Question 20 :
Determine the nature of roots of the given equation from its discriminant.<br/>$x^{2}\, +\, 3\sqrt2x\, -\, 8\, =\, 0$
Question 21 :
If the equation $x^2- m (2x - 8) - 15 = 0$ has equalroots, then $m =$
Question 22 :
The set of values of '$p$' for which the expression $x^2-2px+3p+4$ is negative for at least one real $x$ is-
Question 23 :
Assertion (A): The roots of $(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$  are real<br/>Reason (R): A quadratic equation with non-negative discriminant has real roots .<br/>
Question 24 :
If $\alpha $ and $\beta$ are roots of $x^{2}$ - $(k + 1)$ $x$ + $\dfrac{1}{2}$ $(k^{2}+k+1)$ $=$ 0, then $\alpha ^{2}+\beta ^{2}$ is equal
Question 25 :
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 26 :
For the equations $x^2+ bx + c = 0$ and $2x^2+ (b + 1)x + c + 1 = 0$ select the correct alternative
Question 27 :
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 28 :
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 29 :
If $\displaystyle px^{2}+qx+r=0$ has no real roots and $p,q,r$ are real such that $p+r> 0$, then
Question 30 :
$|x^2 + 6x + p| = x^2 + 6x + p$ $\forall x \in R$ where p is a prime number then least possible value $p$is