Find the two roots of each of the following functions that

. 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 = ______.

Solution

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