Question 1 :
Check whether the following is a quadratic equation.$(x - 3) (2x + 1) = x (x + 5)$<br/>
Question 5 :
Choose the best possible answer<br/>$\displaystyle 32{ x }^{ 2 }-6=\left( 4x+10 \right) \left( 10x-6 \right) $ is quadratic equation <br/>
Question 6 :
If the roots of the equation $ax^2+bx+c=0$ are all real equal then which one of the following is true?
Question 7 :
Find the quadratic equation in $x$, whose solutions are $3$ and $2$.
Question 8 :
Squaring the product of $z$ and $5$ gives the same result as squaring the sum of $z$ and $5$. Which of the following equations could be used to find all possible values of $z$?
Question 10 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 11 :
The mentioned equation is in which form?<br/>$(y\, -\, 2)\, (y\, +\, 2)\, =\, 0$
Question 12 :
Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.
Question 13 :
If $p$ is chosen at random in the interval $0 \le p \le 5$,the probability that the equations $x^{2}+px+p/4+1/2=0$ are real is
Question 14 :
If $x - 4$ is one of the factor of $x^{2} - kx + 2k$, where $k$ is a constant, then the value of $k$ is
Question 15 :
Which of the following is a quadratic polynomial in one variable?<br>
Question 16 :
If $C > 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then
Question 17 :
If $ax^2 + bx + c =0$ has equal roots, then c is equal to ______.
Question 18 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 19 :
Check whether the given equation is a quadratic equation or not.<br/>$\quad { x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } } =2\quad $<br/>
Question 20 :
The nature of the roots of a quadratic equation is determined by the:<br>
Question 21 :
The roots of the following quadratic equations are real and distinct.<br/>$(x - 2a) (x - 2b) = 4ab$
Question 23 :
If the roots of the equation<br>$a(b-c)x^2+b(c-a)x+c(a-b)=0$ are equal, then which one of the following is correct ?
Question 24 :
If, in the expression $x^2 - 3$, x increases or decreases by a positive amount a, the expression changes by an amount
Question 26 :
For what values of $k$, the equation $x^{2}+2(k-4)x+2k=0$ has equal roots?
Question 27 :
Obtain a quadratic equation whose roots are reciprocals of the roots of the equation $x^2-3x - 4 =0$.
Question 28 :
A quadratic equation in $x$ is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and the other condition is<br/>
Question 29 :
Applying zero product rule for the equation $x^{2}- ax - 30 = 0$ is $x = 10$, then $a =$ _____.<br/>
Question 30 :
Which one of the following condition will satisfy the zero product roots of the equation $(x - a)(x - b)$?<br>
Question 31 :
The number of values of $k$ for which $\displaystyle \left \{x^{2}-(k-2)x+k^{2}\right\}+ \left \{x^{2}+kx+(2k-1)\right \}$ is a perfect square is/are
Question 32 :
If the equations $x^{2}+ax+bc=0$ and $x^{2}+bx+ca=0$ have a common root, then their other roots satisfy the equation<br>
Question 33 :
If the roots of the quadratic equation $ x^{2}-4x-\log_{3}a=0 $ are real, then the least value of $a$ is
Question 34 :
In each of the following, determine whether the given values are solutions of the given equation or not :<br/> $x^2 \, - \, 3\sqrt{3x} \, + \, 6 \, = \, 0, \, x \, = \, \sqrt{3}, \, x \, = \, -2\sqrt{3}$
Question 35 :
$|x^2 + 6x + p| = x^2 + 6x + p$ $\forall x \in R$ where p is a prime number then least possible value $p$is
Question 36 :
If $(x-a)(x-5)+2=0$ has only integral roots where $ a\in I,$ then value of 'a' can be:<br>
Question 37 :
In each of the following, determine whether the given values are solutions of the given equation or not :<br/> $x \, + \, \dfrac{1}{x} \, = \, \dfrac{1}{6}, \, x \, = \, \dfrac{5}{6}, \, x \, = \, \dfrac{4}{3}$
Question 38 :
Let $a$ and $b$ be two distinct roots of the equation $x^3+3x^2-1=0$. The equation on which has $(ab)$ as its root is equal to
Question 39 :
In the following, determine whether the given quadratic equation have real roots and if so, find the roots :<br/>$\sqrt{3}x^2 \, + \, 10x \, - \, 8\sqrt{3} \, = \, 0$
Question 40 :
The expression $ax+b$ is equal to $13$ when $x$ is $5$ and to $25$ when $x$ is $13$. Find the value of the expression when $x$ is $0.5$
Question 41 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 42 :
lf $\mathrm{a},\ \mathrm{b},\ \mathrm{c}$ are in G.P. then the equations $\mathrm{a}\mathrm{x}^{2}+2\mathrm{b}\mathrm{x}+\mathrm{c}=0$ and $\mathrm{d}\mathrm{x}^{2}+2\mathrm{e}\mathrm{x}+\mathrm{f}=0$ have a common root if $\dfrac { d }{ a } ,\dfrac { e }{ b } ,\dfrac { f }{ c } $ are in <br/>
Question 44 :
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 
Question 45 :
Two roots of $4x^3 + 8x^2+ Kx - 18 = 0$ are equal numerically but opposite in sign. Find the value of K.
