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

In the following questions, two equations numbered I and II are given. You have to solve both the equations and Give an answer If

$\left(1\right)$$x > y$

$\left(2\right) x \ge y$

$\left(3\right) x< y$

$\left(4\right) x \le y$

$\left(5\right) x = y$  Or the relationship cannot be established

I. $2x + 3y = 19$
II.$3x - 2y = 9$

$\left(1+m^2\right)x^2+2 mcx+c^2-a^2=0$ has equal roots if ________.

The sum of two numbers is $15$ and the sum of their squares is $113$. The numbers are

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.$20y^2-y-12 = 0$

If $\left(–4\right)$ is one root of the equation $x^2+px-4=0$ and the equation $x^2+px+q=0$ has equal roots then the value of $p$ and $q$ are respectively.

A two-digit number is such that the product of the digits is $8$ and when $18$ is added to the number, the number is reversed. The number 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. $x^2-14x+48=0$
II.$y^2-y-30=0$

In the following question, two equations numbered I and II are given. You have to solve both the equations 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.$\frac{6}{\sqrt{x}} + \frac{14}{\sqrt{x}} = 10$

II.$\frac{\sqrt{y}}{2} + \frac{\sqrt{y}}{3} = \frac{5}{2}$

$\frac{\sqrt{x+4}+\sqrt{x-4}}{\sqrt{x+4}-\sqrt{x-4}}=2$ ,find the value of $x$?

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 $\frac{2x^2+3x+4}{x^2+x+3}?$

Which of the following equations has real roots$?$