Quadratic Equation Easy Questions and Answers

Correct Option: C

Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
∴ Area = Length × Breadth = x(x + 8)m² But the area of the plot is given to be 308 m²
∴ x( x + 8 ) = 308 ⇒ x² + 8x - 308 = 0
⇒ x² + 22x - 14x - 308 = 0
⇒ x( x + 22 ) - 14 ( x - 22 ) = 0
⇒ ( x + 22 ) ( x - 14 ) = 0
⇒ x = 14, -22
But, x = −22 is not possible, since breath cannot be negative
∴ x = 14
Hence the breadth of the rectangular plot = 14 m Length of the rectangular plot = (14 + 8) m = 22 m.

We can say that ,

Putting in above equation , x -	1	= y
	x

∴

x +

= x² +

+ 2 =

x +

+ 4 = y² + 4

x²

Correct Option: C

We can say that ,

Putting in above equation , x -	1	= y
	x

∴

x +

= x² +

+ 2 =

x +

+ 4 = y² + 4

x²

So, given equation becomes

⇒ y		y -	3		= 0 ⇒ y = 0 or y =	3
			2			2

∴ x -	1	= 0 ⇒ x -	1	=	3
	x		x		2

⇒ x² - 1 = 0 or 2x² - 3x - 2 = 0
⇒ x = ± 1 or ( 2x + 1 ) ( x - 2 ) = 0
⇒ x = ± 1 or - 1/2 or x = 2.
Thus , option C is correct answer .

As we can say that ,
From equation Ⅰ. 18x² + 18x + 4 = 0
⇒ 18x² + 12x + 6x + 4 = 0
⇒ 6x(3x + 2) + 2(3x + 2) = 0

From equation Ⅱ.
12y² + 29y + l4 = 0
⇒ 12y² + 21y + 8y + 14 = 0

Correct Option: D

As we can say that ,
From equation Ⅰ. 18x² + 18x + 4 = 0
⇒ 18x² + 12x + 6x + 4 = 0
⇒ 6x(3x + 2) + 2(3x + 2) = 0
⇒ (6x + 2)(3x + 2) = 0

⇒ x = -	1	, -	2
	3		3

From equation Ⅱ. 12y² + 29y + l4 = 0
⇒ 12y² + 21y + 8y + 14 = 0
⇒ 3y(4y + 7) + 2(4y + 7) = 0
⇒ (3y + 2)(4y + 7) = 6

⇒ y = -	2	, -	7
	3		4

From above equations we can say that x ≥ y is correct answer .

(x - 1) (2x - 5) = 0 ⇒ x = 1, 5/2
So, its roots are real.

Correct Option: B

(x - 1) (2x - 5) = 0 ⇒ x = 1, 5/2
So, its roots are real.

Given equation is 2x² - 9x - 18 = 0
[by factorisation method]
⇒ 2x² - 12x + 3x - 18 = 0

Correct Option: C

Given equation is 2x² - 9x - 18 = 0
[by factorisation method]
⇒ 2x² - 12x + 3x - 18 = 0
⇒ 2x(x - 6) + 3(x - 6) = 0
⇒ (2x + 3) (x - 6) = 0
∴ x = -3/2, 6

	x +	1		²	-	3		x -	1		= 4 is :
		x				2			x