17
1 If: y = 4x2-12x-3 and y = x2+11x+5 2 Then: 4x2-12x-3 = x2+11x+5 3 And so: 3x2-23x-8 = 0 4 Using the quadratic equation formula: x = -1/3 or x = 8 5 By substitution they intersect at: (-1/3, 13/9) and (8, 157) 6 Length: square root of (-1/3-8)2+(13/9-157)2 = 155.7786099 7 Distance between intersections: 155.779 rounded to 3 decimal places
12x^3+17x^2+5x=0x(12x^2+17x+5)=0x(x+1)(12x+5)=0x=0x=-1x=-5/12
3x-8+5x+39+4x+51 = x(3+5+4) + -8 + 39 + 51 = 12x +82
(2x - 5)(2x - 5) or (2x - 5) squared
4x2 + 12x + 5 = (2x + 1)(2x + 5).
4x2 + 12x + 5 = 4x2 + 2x + 10x + 5 = 2x(2x+1) + 5(2x+1) = (2x+1)(2x+5)
(2x+5)(2x+1)
The factors of 5 are 1 and 5. 12 = 2 x 5 + 2 x 1, therefore: 4x2 +12x +5 = (2x + 1)(2x + 5)
x2+12x+5 = 3 x2+12x+5-3 = 0 x2+12x+2 = 0
x=5
30+12x = 6(5+2x)
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x2-5-4x2+3x = 0 -3x2+3x-5 = 0 or as 3x2-3x+5 = 0
8x-3+6x-1 = 12x+614x-4 = 12x+614x-12x = 6+42x = 10x = 5
-5 + 12x = 18x + 7Subtract 7 from each side:-12 + 12x = 18xSubtract 12x from each side:-12 = 6xDivide each side by 6:-2 = x
2x+5=-91-10x 12x+5=-91 12x=-96 x=-8