find the length and the breadth of a room which satisfies the equation 2x^2+x-300=0
Answers
Answer :
12 units
Step-by-step explanation :
Given quadratic equation,
2x² + x - 300 = 0
It is of the form ax² + bx + c = 0
we know,
quadratic term = ax²
linear term = bx
constant term = c
Hence for the given quadratic equation,
Quadratic term = 2x²
Linear term = x
Constant term = -300
Steps to factorize :
>> Find the product of quadratic term[ax²] and constant term[bx]
= 2x² × (-300)
= -600x²
>> Find the factors of ''-600x²'' in pairs,
(x) (-600x)
(-x) (600x)
(2x) (-300x)
(-2x) (300x)
(3x) (-200x)
(-3x) (200x)
(4x) (-150x)
(-4x) (150x)
(5x) (-120x)
(-5x) (120x)
(6x) (-100x)
(-6x) (100x)
(8x) (-75x)
(-8x) (75x)
(10x) (-60x)
(-10x) (60x)
(12x) (-50x)
(-12x) (50x)
(15x) (-40x)
(-15x) (40x)
(24x) (-25x)
(-24x) (25x)
(30x) (-20x)
(-30x) (20x)
>> From the above, find the pair that adds to get linear term[bx]
25x - 24x = x
>> Split x as 25x and -24x
2x² + x - 300 = 0
2x² - 24x + 25x - 300 = 0
>> Find the common factor
2x(x - 12) + 25(x - 12) = 0
(x - 12) (2x + 25) = 0
=> x - 12 = 0 ; x = 12
=> 2x + 25 = 0 ; x = -25/12
The dimensions of the room can't be negative.
Hence, x = 12
Therefore, the length and breadth of the room = 12 units