Question 2 234 9 marks No explanatory concluding sentences a

Question 2 (2+3+4 9) marks No explanatory concluding sentences are required for any part of this question (a) Solve the following linear equation: 2 (r 3.5) --3a 8. (b) By factorisation, find all solutions to the following equation: (c) Using the quadratic formula, find all solutions to the following equation. Give your answers to one decimal place. T2 51.84 14.4r

Solution

a)

2( x+ 3.5 ) = -3x - 8

2 x + 7 = -3x - 8

2x+ 3x = -8-7

5x = -15

x = -15/5

x = -3

b)

x^2 - 2x = 42 -x

x^2 -2x +x -42 = 0

x^2 -x -42 = 0

x^2 -6x + 7x - 42 = 0

x(x-6) + 7 (x-6) = 0

(x+7) (x-6) = 0

x = -7 and x = 6 are the solutions for the equation x^2 - 2x = 42 -x

c)

x^2 + 51.84 = 14.4x

=> x^2 - 14.4x + 51.84 = 0

Using quadratic formula , the roots are

x = (-b + (b^2-4ac)^(1/2))/2a and    (-b - (b^2-4ac)^(1/2))/2a

from the equation

a = 1 , b = -14.4 , c = 51.84

substituting in the formula we get

x = (14.4+0 )/2 and x = (14.4 -0)/2

x = 7.2 is the only solution for the given equation