Question 1 :
Is the following equation a quadratic equation?$16x^2 - 3 = (2x + 5) (5x - 3)$

Question 2 :
Which point satisfies the linear quadratic system y=x+3 and y=5-x$\displaystyle ^{2}$?

Question 4 :
The least integer $'c'$ which makes the roots of the equation $x^2+3x+2c$ imaginary is

Question 7 :
Is the following equation a quadratic equation?$\displaystyle \frac{3x}{4} - \frac{5x^2}{8} = \frac{7}{8}$

Question 9 :
The difference between the product of the roots and the sum of the roots of the quadratic equation $6x^{2} - 12x + 19 = 0$ is

Question 10 :
__________ is true for the discriminant of a quadratic equation $x^2+x+1=0$.

Question 12 :
If $3$ is one of the roots $x^2-mx+15=0$. Choose the correct options -<br/>

Question 13 :
If $b_1b_2=2(c_1+c_2)$, then at least one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has

Question 15 :
If $\alpha , \beta , \gamma $ are the real roots of the equation $x^{3}-3px^{2}+3qx-1=0$, then the centroid of&#160;the triangle with vertices $\displaystyle \left ( \alpha , \frac{1}{\alpha } \right )$, $\left ( \beta , \dfrac{1}{\beta } \right )$ and $\displaystyle \left ( \gamma , \frac{1}{\gamma } \right )$ is at the point

Question 16 :
I: If $a,b,c$ are real, the roots of $(b-c)x^{2}+(c-a)x+(a-b)=0$ are real and equal, then $a, b, c$ are in A.P.<br>II: If $a, b, c$ are real andthe roots of$(a^{2}+b^{2})x^{2}-2b(a+c)x+b^{2}+c^{2}=0$ are real and equal, then $a, b,c$ are in H.P.<br>Which of the above statement(s) is(are) true?<br>

Question 17 :
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 18 :
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 19 :
Find the discriminant of the equation and the nature of roots. Also find the roots.$2x^2 + 5 \sqrt 3x + 6 =0$

Question 20 :
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?<br><br>

Question 21 :
If the roots of the equation&#160; $ \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 23 :
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 :

Question 24 :
The quadratic equation $p(x) =0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x)) =0$ has