The given equation is
x² - 5x + 6 = 0 ⇒ x² - 2x - 3x + 6 = 0
⇒ x( x - 2 ) - 3( x - 2 ) = 0
⇒ ( x - 2 ) ( x - 3 ) = 0
⇒ x - 2 = 0 or x - 3 = 0

Correct Option: A

The given equation is
x² - 5x + 6 = 0 ⇒ x ² - 2x - 3x+ 6 = 0
⇒ x( x - 2 ) - 3( x - 2 ) = 0
⇒ ( x - 2 ) ( x - 3 ) = 0
⇒ x - 2 = 0 or x - 3 = 0
⇒ x = 2 or x = 3
Thus, the other root of the given quadratic equation is 2.

Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x² − (sum of the roots) x + (product of the roots) = 0

Correct Option: A

Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x² − (sum of the roots) x + (product of the roots) = 0
⇒ x² - 6x - 16 = 0

According to question ,we can say that
Ⅰ. 4x + 7y = 209 ..........................( 1 )
Ⅱ. 12x − 14y = − 38 .................... ( 2 )
Multiplying (1) by (2):
8x + 14y = 418 ................(3)
Adding (2) and (3):
20x = 380 ⇒ x = 19

Correct Option: E

According to question ,we can say that
Ⅰ. 4x + 7y = 209 ...............( 1 )
Ⅱ. 12x − 14y = − 38 .................... ( 2 )
Multiplying (1) by (2):
8x + 14y = 418 ................(3)
Adding (2) and (3):
20x = 380 ⇒ x = 19
Substituting the value of x in (1), we get
76 + 7y = 209
⇒ 7y = 133 ⇒ y = 19
From above equations it is clear that x = y is correct answer .

Quadratic equation must be in the form of ax² + bx + c = 0, where a ≠ 0.

Correct Option: C

Clearly, 7x² = 49 or 7x² - 49 = 0, which is of the form ax² + bx + c = 0, where b = 0.
Thus, 7x² - 49 = 0 is a quadratic equation.

According to question , we have
From equation Ⅰ.
8x² + 6x - 5 = 0
⇒ 8x² + 10x − 4x − 5 = 0
⇒ 2x(4x + 5) − 1(4x + 5) = 0

From equation Ⅱ.
12y² − 22y + 8 = 0
⇒ 12y² − 16y − 6y + 8 = 0

Correct Option: C

According to question , we have
From equation Ⅰ. 8x² + 6x - 5 = 0
⇒ 8x² + 10x − 4x − 5 = 0
⇒ 2x(4x + 5) − 1(4x + 5) = 0
⇒ (2x − 1)(4x + 5) = 0