Question 1 :
If roots of $(a - 2b + c)x^2 + (b - 2c +a)x + (c - 2a +b) = 0$ are equal, then :
Question 3 :
Solve the following quadratic equation by factorization :<br>$a(x^2 \, + \, 1) \, - \, x \, (a^2 \, + \, 1) \, = \, 0$
Question 5 :
Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.
Question 6 :
The nature of the roots of a quadratic equation is determined by the:<br>
Question 8 :
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 9 :
For what values of $k$, the equation $x^{2}+2(k-4)x+2k=0$ has equal roots?
Question 10 :
Which one of the following condition will satisfy the zero product roots of the equation $(x - a)(x - b)$?<br>
Question 11 :
The following equation is a qudratic equation. $16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$
Question 12 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 16 :
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 17 :
The value of k for which the equation $x^{2} - 4x + k = 0 $ has equal roots is<br/>
Question 19 :
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 20 :
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 21 :
The roots of $a{ x }^{ 2 }+bx+c=0$, where $a\neq 0,b,c\epsilon R$ are non real complex and $a+c<b$. Then <br><br>
Question 22 :
If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then<br/>
Question 23 :
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 25 :
If one of roots of $x^2+ ax + 4 = 0$ is twice the other root, then the value of 'a' is .
Question 26 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.Let $\alpha ,\beta $ be roots of quadratic equation. If there are at least four negative integers between $\alpha$ and $\beta$, then the complete set of values of $a$ is
Question 27 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 28 :
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 29 :
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 30 :
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 31 :
Let $f: R\rightarrow R $ be the function $f(x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3})+ (x - x_{3})(x-x_{1})$ with $a_{1}, a _{2}, a_{3}\in R $ Then $f(x)=\geq 0 $if and only if<br>
Question 32 :
The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>
Question 33 :
A company wants to know when the sale of their product reaches a profit level of Rs. $1000$. The revenue equation is R $=$ $200x-0.5x^{2}$, and the cost to produce x product is determined with $C = - 6000 - 40x$. How many products have to be produced and sold to net a profit of Rs. $1000$?<br/>
Question 35 :
If one of the roots of the quadratic equation $a{ x }^{ 2 }-bx+a=0$ is $6$, then the value of $\cfrac { b }{ a } $ is equal to