Question

]One solution of the equation 3x^2 − 16x + 5 = 0 is 1/3. What is the other solution?

Answer 1

well it factors to

(3x - 1)(x - 5) = 0

just find the solutions..

Answer 2

wait. wouldn't the 3 be outside of the parentheses, and doesn't the factors have to be added up to -16?

Answer 3

well just distribute and see if you get the original equation...

Answer 4

*looks down at the ground* :3 maybe i got back to the original problem, maybe i didn't.. :3. How come math people are so smart??? @campbell_st

Answer 5

so the other solution is x = -5?

Answer 6

its all about practice and identifiying...

here is how I factored this equation

works everytime

if you have a quadratic

\[ax^2 + bx + c = 0\]

start with a*c in your question 3 times 5 = 15

find factors that add to -16, -15 and -1

then you set up the brackets for the binomials

(ax + factor 1)(ax + factor 2) (3x -15)(3x -1)
-------------------------- = -------------- =0
a 3

check for common factors

3(x - 5)(3x -1)
-------------- = 0
3

a factor of 3 cancels... this will happen every time

leaving (x -5)(3x -1) = 0

so you need to solve

x - 5 = 0

3x - 1 = 0

to find the solutions to the equation.

Answer 7

so the solutions are 1/3 and -5?

Answer 8

not -5

x - 5 = 0

x = 5 makes the equation true.

Answer 9

oops meant +5*