This assignment exercises your knowledge of fundamental algebra. Rusty algebra g
ID: 1166782 • Letter: T
Question
This assignment exercises your knowledge of fundamental algebra. Rusty algebra gives more problems than economics. You are hereby warned that some problems have nice, clean answers and some do not (even if calculations are carried to several decimal places). Please carry out calculations to two decimals before rounding off, as a general rule. Also, please show your work where possible.
4. Find the two roots of each of the following functions (that is find the two X values that make Y = 0). This skill may be useful in assignment 11. EXAMPLE: Y = 3X2 -11X +6 is the product of (3X -2)(X -3). If you let Y = 3X-2 then X = 2/3 will make Y = 0. If you let Y = X-3 then X = 3 will make Y = 0. Thus both X = 2/3 and X = 3 are roots. Show the algebra involved.
a. Y = -6X2 -5X +6. The two roots are X = ______ and X = ______.
b. Y = 345 +8X –X2. The two roots are X = ______ and X = ______.
Explanation / Answer
Answer:-
?a)
Y = -6X^2 -5X +6.
= - (6X^2 + 5X -6.)
= - (6x^2+9x-4x-6)
= - (3x(2x+3) - 2 (2x+3))
= - (2x+3)(3x-2)
So roots are:
x = -3/2 and x=2/3
?b)
Y = 345 +8X –X2
Y = - (x^2 -8x - 345)
= -(x^2 -23x + 15x - 345)
= - (x (x-23) + 15(x-23))
= - (x-23)(x+15)
roots are x=23 and x=-15