Column 1
2x3 –6x2 +x = 5
x = 3
x5 - 3x3 + 2x = 0
x(x2 - 1)(x2 - 2) = 0 —>
x1 = -1
x2 = 0
x3 = 1
x4 = square root of 2
x5 = minus square root 2
x2 + 2x3 - 8x2 = 0
x2(1+2x-8) = 0 —>
x1 = 0
x2 = 7/2
Paul sold two fifths of his comic collection and then bought 100 more. After doing this, he had the same number of comics that he would have had if he had not sold any and had bought 40 more. How many did he originally have?
(x - 2/5x) + 100 = x + 40 ———> 150 copies
x4 - 2x3 + 3 = -x3 + 3
x3(x - 1) = 0
x1 = 0
x2 = 1
9x6 - 37x4 + 4x2 = 0
x2(9x2 - 1)(x2 - 4) = 0 —>
x1 = -2
x2 = -1/3
x3 = 0
x4 = 1/3
x5 = 2
x4 - 2x3 + x2 = 0
x2(x2 - 2x + 1) = 0 —>
x2 = 1
Claudia is 26 years younger than her mother. How old are they now if in ten years, Claudia’s mother will be three time older than Claudia
x + 36 = 3(x + 10) → x + 36 = 3x + 30 → x = 3
Claudia is 3 years old, and her mother is 29 years old.
x3 - 4x2 - 4x + 16 = 0
(x - 4)(x2 - 4) = 0
x1 = -2
x2 = 2
x3 = 4
x4 + 7x3 + 15x2 + 9x = 0
x(x + 1)(x + 3)2 = 0 —>
x1 = -3
x2 = -1
x3 = 0
2x3 - 3x = 2x + x3
x(x2 - 5) = 0 —>
x1 = 0
x2 = minus square root of 5
x3 = Square root of 5
On a journey, there have been two stops. Before the first one, a third of the journey had been completed. Between the first and the second stop, another fifth of the journey was completed.
From the second stop to the end, there are 210 km. What is the total distance that has been travelled?
x/3 + x/5 + 210 = x ——> 5x + 3x 3 150 = 15x
x = 450km
4x5 + 8x4 - 5x3 = 10x2 - x - 2
(2x - 1)(x - 1)(x + 1)(x + 2)(2x + 1) = 0 —>
x1 = -2
x2 = -1
x3 = 1
x4 = -1/2
x5 = 1/2
3x4 - 16x2 + x = 2x4 + x
x2(x2 - 16) = 0 —>
x1 = -4
x2 = 0
x3 = 4
2x3 - 11x2 + 12x = 0
x(2x2 - 11x + 12) = 0 —>
x1 = 0
x2 = 3/2
x3 = 4
The area of a rectangle is 96 cm2. Find the dimensions of the rectangle given that it is 4 cm longer than it is wide.
Width in cm=x → Length in cm = x+4
x · (x + 4) = 96 → x2 + 4x – 96 = 0 →
x = (−4 ± √400)/2 = {x1 = 8}{x2=-12}
Ignoring the negative solution, the width is 8 cm and the length is 12 cm.