Question 2 :
Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.
Question 3 :
Choose best possible option.<br>$\displaystyle\left( x+\frac { 1 }{ 2 } \right) \left( \frac { 3x }{ 2 } +1 \right) =\frac { 6 }{ 2 } \left( x-1 \right) \left( x-2 \right)$ is quadratic.<br>
Question 4 :
Is the following equation a quadratic equation?$\displaystyle 3x + \frac{1}{x} - 8 = 0$
Question 6 :
State the following statement is True or FalseThe length of a rectangle ($x$) exceeds its breadth by $3$ cm. The area of a rectangle is $70$ sq.cm, then the equation is $x\, (x\, -\, 3)\, =\, 70$.<br/>
Question 7 :
Which of the following is a quadratic polynomial in one variable?<br>
Question 8 :
The sum of a number and its reciprocal is$ \displaystyle \frac{125}{22} $ The number is
Question 12 :
If $y=\cfrac { 2 }{ 3 } $ is a root of the quadratic equation $3{ y }^{ 2 }-ky+8=0$, then the value of $k$ is ..................
Question 14 :
The discriminant of $x^2 - 3x + k = 0$ is 1 then the value of $k = .............$
Question 16 :
Say true or false.<br/>If $x(x - 4) = 0$, then $x= 0$ or $x=4$.<br/>
Question 17 :
The mentioned equation is in which form?<br/>$(y\, -\, 2)\, (y\, +\, 2)\, =\, 0$
Question 20 :
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 21 :
If a, b, c $\epsilon\ Q\ $, then the roots of the equation $(b + c - 2a) x^{2} + (c+a-2b) x+ (a+b-2c) = 0$ are<br/>
Question 23 :
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 24 :
The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :<br/>
Question 25 :
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 26 :
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 27 :
The quadratic $x^2+ax+b+1=0$ has roots which are positive integers, then $(a^2+b^2)$ can be equal to
Question 28 :
If both a and b belong to the set $\displaystyle \left\{ 1,2,3,4 \right\}$ then the number of equations of the form $ ax^{2}+bx+1=0$ having real roots is :<br>
Question 29 :
If the roots of the equation  $ \dfrac { { 1 } }{ x+p } +\dfrac { 1 }{ x+q } =\dfrac { 1 }{ r } $ are equal in magnitude but opposite in sign, then which of the following are true?<br/>
Question 30 :
The values of $a$ which makes the expression $x^2 -ax + 1 -2a^2$ always positive for real values of $x$ are
Question 31 :
Assertion: If $a + b + c = 0$ and $a, b, c$ are rational, then the roots of the equation $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ are rational .
Reason: Discriminant of $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ is a perfect square .
Question 32 :
If $x=1+i$ is a root of the equation $x^3-ix+1-i=0$, then the other real root is
Question 33 :
For what value of k will$\displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11$ have equal roots?
Question 34 :
Determine the nature of roots of the given equation from its discriminant.<br/>$x^{2}\, +\, 3\sqrt2x\, -\, 8\, =\, 0$
Question 35 :
What is the smallest integral value of $k$ such that $2x (kx - 4) - x^{2} + 6 = 0$ has no real roots?
Question 36 :
The condition for the equations $ax^{2} + bx + c = 0$ and $a'x^{2} + b'x + c' = 0$ to have reciprocal roots is $\dfrac{a}{c'}=\dfrac{b}{b'}=\dfrac{c}{a'}$<br/>
Question 37 :
The values of k for which the roots are real and equal of the following equation $x^2 - 2(5 + 2k)x + 3(7 + 10k) = 0$ are $k = 2, \dfrac{1}{2}$
Question 38 :
Which of the following equations has no solution for $a$ ?
Question 39 :
If k be the ratio of the roots of the equation$ \displaystyle x^{2}-px+q=0 $ , the value of$ \displaystyle \frac{k}{1+k^{2}} $ is
Question 40 :
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 41 :
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 42 :
Find the roots of equation:<br>$\displaystyle{ x }^{ 2 }-\frac { 1 }{ 12 } x-\frac { 1 }{ 12 } =0$<br>
Question 43 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 44 :
Let $f(x)\, =\, x^2\, +\, ax\, +\, b,$ where a, b $\epsilon$ R. If $f(x) = 0$ has all its roots imaginary, then the roots of $f(x) + f' (x) + f" (x) = 0$ are
Question 45 :
If the equations ${x}^{2}+ax+12=0$, ${x}^{2}+bx+15=0$ and ${x}^{2}+(a+b)x+36=0$ have a common root then the possible values of $a,b$ is (are)
Question 46 :
If $\tan \dfrac {\alpha}{2}$, and $\tan \dfrac {\beta}{2}$ are the roots of $8x^{2} - 26x + 15 = 0$, then $\cos (\alpha + \beta)$ is equal to
Question 47 :
If $\displaystyle r_{1}\:$ and $ r_{2}$ are the roots of $\displaystyle x^{2}+bx+c=0$ and $\displaystyle S_{0}=r_{1}^{0}+r_{2}^{0}$, $\displaystyle S_{1}=r_{1}+r_{2}$ and $\displaystyle S_{2}=r_{1}^{2}+r_{2}^{2}$, then the value of $\displaystyle S_{2}+bS_{1}+cS_{0}$ is
Question 48 :
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 49 :
The roots of $(x-a)(x-c)+k(x-b)(x-d)=0$ are real and distinct for all real $k$ if<br>
Question 50 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
