Solution of Quadratic Equations

In the following questions, two-equation numbered I and II are given. You have to solve the equation and give the answer if-

$1. x > y$
$2. x \ge y$
$3. x < y$
$4. x \le y$
$5. x= y$Or the relationship cannot be established.

I.$3x^2-47x+184 = 0$
II.$2y^2-23y+66 = 0$

If the roots of the equation${\mathrm{x}}^2+2(3\mathrm{a}+5)\mathrm{x}+2(9{\mathrm{a}}^2+25)=0$ are rational, then the value of $\mathrm{a}$ is _____.

In the following questions, two-equation numbered I and II are given. You have to solve the equation and give the answer if-

$$\begin{gathered} 1. x > y \\ 2. x\ge y \\ 3. x < y \\ 4. x \le y \end{gathered}$$
$5. x = y$  Or the relationship cannot be established.

I. $x^2-10\sqrt{3}x+63=0$
II.$y^2-\sqrt{2}y-24=0$

In each of the following questions, two equations are given. You have to solve them and find the relation between $p$ and $q$
 

I.$6p^2+5p+1=0$

II.$20q^2+9q=-1$

In the question, two equations (I) and (II) are given. You have to solve both the equations and give the answer.

(A) If $x>y$

(B) If $x<y$

(C) If$x\ge y$

(D) If $x\le y$

(E) If $x=y$ or there is no relationship.

If x is real, the minimum value of 4x ² + 4 x+ 9 is

Quadratic equation corresponding to the roots $2+\sqrt{5} \& 2-\sqrt{5}$ is ______.

In the following questions, two equations numbered I and II are given. You have to solve the equation and give the answer if-

$1. x > y$
$2. x \ge y$
$3. x < y$
$4. x \le y$
$5. x = y$  Or the relationship cannot be established.

I. $x^2-8x+16 = 0$
II.$20y^2-y-12 = 0$

In the following questions, two-equation numbered I and II are given. You have to solve the equation and give the answer if-

$$\begin{gathered} 1. x > y \\ 2. x \ge y \\ 3. x < y \\ 4. x\le y \end{gathered}$$
$5. x = y$ Or the relationship cannot be established.

I. $x^2-14x+48=0$
II.$y^2-y-30=0$

In each of the following questions, two equations are given. You have to solve them and find out the relation between $a$ and $b$:

I. $a^2+6a+9=0$
II. $b^2+8b+16=0$

Find the maximum value of $\frac{2x^2+3x+4}{x^2+x+3}?$

In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer if
1) if $x>y$
2) if $x\ge y$
3) if $x<y$
4) if $x\le y$
5) if $x=y$ or the relationship cannot be established.

I.$x² – 19x + 84 = 0$
II. $y² – 25y + 156 = 0$

In the following questions two equation numbered I and II are given. You have solve the equation and give answer if-
$1$. x $>$ y
$2$. x $\ge$ y
$3$. x $<$y
$4$. x $\le$ y
$5$. x $=$ y or the relationship cannot be established.
I. $20x^2 -31x +12=0$
II. $20y^{2 }-y-12=0$

The sum of the squares of two consecutive natural numbers is $61$. The numbers are _____

In each of the following questions, two equations are given. You have to solve them and find the relation between $p$ and $q$?

I.$3p² + 15p = - 18$
II. $q² + 7q + 12 = 0$

In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer if
1) if $x > y$
2) if$x \ge y$
3) if $x < y$
4) if $x \le y$
5) if $x = y$ Or the relationship cannot be established.

I. $\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$
II.$y^5 - \frac{{\left(2 \times 14\right)}^{{\displaystyle \frac{11}{2}}}}{\sqrt{y}} = 0$

Read the following Radar graph carefully and answer the questions given below. Number of motorvehicles produced by different companies in 3 years (in thousands)

The number of motor vehicles produced by Honda is what percent of that by Maruti?

In the following question, two equations numbered I and II are given. You have to solve both the equation and give the answer.
1. if $x>y$
2. if $x\ge y$
3. if $x<y$
4. if $x\le y$
5. if $x=y$ or the relationship cannot be established.

I) $20x-43\sqrt{x}+21=0$

II) $y^2-7y+10=0$