Question 1 :
If $C > 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then
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 :
If $3$ is one of the roots $x^2-mx+15=0$. Choose the correct options -<br/>
Question 5 :
The sum of a number and its reciprocal is$ \displaystyle \frac{125}{22} $ The number is
Question 6 :
For the expression $ax^2 + 7x + 2$ to be quadratic, the necessary condition is<br>
Question 7 :
Check whether the given equation is a quadratic equation or not.<br/>$3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$
Question 8 :
Is the following equation a quadratic equation?$16x^2 - 3 = (2x + 5) (5x - 3)$
Question 9 :
The following equation is a qudratic equation. $16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$
Question 10 :
Roots of the equation $\sqrt {\dfrac {x}{1-x}}+\sqrt {\dfrac {1-x}{x}}=2\dfrac {1}{6}$ are
Question 11 :
Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>
Question 12 :
If c is small in comparision with l then ${\left( {\frac{l}{{l + c}}} \right)^{\frac{1}{2}}} + {\left( {\frac{l}{{l - c}}} \right)^{\frac{1}{2}}} = $
Question 13 :
Obtain a quadratic equation whose roots are reciprocals of the roots of the equation $x^2-3x - 4 =0$.
Question 15 :
Applying zero product rule for the equation $x^{2}- ax - 30 = 0$ is $x = 10$, then $a =$ _____.<br/>
Question 17 :
If the roots of the equation $5{x}^{2}-7x+k=0$ are mutually reciprocal then $k=$
Question 19 :
Difference between the squares of $2$ consecutive numbers is $31$. Find the numbers.
Question 20 :
Check whether the following is a quadratic equation.$(x - 3) (2x + 1) = x (x + 5)$<br/>
Question 24 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then $y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>
Question 26 :
If $\alpha \epsilon \left( -1,1 \right) $ then roots of the quadratic equation $\left( a-1 \right) { x }^{ 2 }+ax+\sqrt { 1-{ a }^{ 2 } } =0$ are
Question 27 :
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 28 :
If $x^2-36=0$, which of the following could be a value of $x$?
Question 29 :
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 30 :
Is the following equation a quadratic equation?$(x + 2)^3 = x^3 - 4$
Question 31 :
Determine the values of $p$ for which the quadratic equation $2x^2 + px + 8 = 0$ has real roots.
Question 32 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.If exactly one root is negative, then the range of $a^2+2a+5$ is
Question 33 :
If $a, b, c \in  Q, $ then roots of $ax^2 + 2(a + b)x (3a + 2b) = 0$ are<br/>
Question 34 :
The values of $a$ which makes the expression $x^2 -ax + 1 -2a^2$ always positive for real values of $x$ are
Question 35 :
For what values of $k$ will the quadratic equation : $\displaystyle { 2x }^{ 2 }-kx+1=0$ have real and equal roots?
Question 37 :
If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then<br/>
Question 38 :
A shopkeeper buys a certain no. of books for Rs. $960$. If the cost per book was Rs. $8$ less, the no. of books that could be bought for Rs. $960$ would be 4 more. Taking the original cost of each book to be Rs. $x$, write an equation in $x$ and solve it.
Question 39 :
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 40 :
If the graph of $f\left(x\right)=x^{2}+\left(3-k\right)x+k,\left(where\ k\in\ R\right)$ lies above and below $x-axis$, then $k$ cannot be
Question 41 :
What is the smallest integral value of $k$ such that $2x (kx - 4) - x^{2} + 6 = 0$ has no real roots?
Question 42 :
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 43 :
If the equations $a{x^2} + bx + c = 0$ and ${x^3} + 3{x^2} + 3x + 2 = 0$ have two common roots, then
Question 44 :
$ { x }^{ 2 }+\left( a-b \right) x+\left( 1-a-b \right) =0$ , $a,b \in R.$ Find the condition on $a$, for which both roots of the equation are real and unequal.<br>
Question 45 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$
