1.) 3x² - 6x - 24 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) -4(x + 2) = 0
(x - 4) (x + 2) = 0
x = 4 OR -2
In short, Your Answer would be: Option C
2.) Expression: x² + 11x + n
For perfect square trinomial, c = (b/2)²
c = (11/2)² = (5.5)² =30.25
In short, Your Answer would be: Option C
3.) x² + 4x - 96 = 0
x² - 8x + 12x - 96 = 0
x(x - 8) 12(x - 8) = 0
(x+12) (x-8) = 0
x = -12 OR 8
In short, Your Answer would be: Option B
4.) D.) There is no solution.
5.) We know, V = l * w * h
w * l = 2720/17 = 160
Let, the width = x
Length = 2x + 4
Then, (x)(2x + 4) = 160
2x² + 4x - 160 = 0
x² + 2x - 80 = 0
x² -8x + 10x - 80 = 0
x(x - 8) 10(x - 8) = 0
(x - 8) (x + 10) = 0
x = 8 OR -10
Length can't be in negative so, -10 is rejected.
Width = 8
Length = 2(8) + 4 = 16+4 = 20
In short, Your Answer would be: Option B
Hope this helps!
