SOLUTION: Given that𝑓 (𝑥) =1/4𝑥^2 and𝑔 (𝑥) =−1+1/3𝑥, find all 𝑥 for which𝑓 (𝑥) =𝑔 (𝑥) .State any

Algebra ->  Test -> SOLUTION: Given that𝑓 (𝑥) =1/4𝑥^2 and𝑔 (𝑥) =−1+1/3𝑥, find all 𝑥 for which𝑓 (𝑥) =𝑔 (𝑥) .State any      Log On


   

Question 1128874: Given that𝑓 (𝑥) =1/4𝑥^2 and𝑔 (𝑥) =−1+1/3𝑥, find all 𝑥 for which𝑓 (𝑥) =𝑔 (𝑥) .State any non-real solutions in the form 𝑎 ± 𝑏𝑖.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%281%2F4%29x%5E2
g%28x%29=-1%2B%281%2F3%29x
find: f%28x%29=g%28x%29

%281%2F4%29x%5E2=-1%2B%281%2F3%29x

%281%2F4%29x%5E2%2B1-%281%2F3%29x=0....each term multiply by 12

12%281%2F4%29x%5E2%2B1%2A12-12%281%2F3%29x=0

cross%2812%293%281%2Fcross%284%29%29x%5E2-cross%2812%294%281%2Fcross%283%29%29x%2B12=0

3x%5E2-4x%2B12=0...use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ..in your case, a=3, b=-4, and c=12

x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A12+%29%29%2F%282%2A3%29+

x+=+%284+%2B-+sqrt%28+16-144+%29%29%2F6+

x+=+%284+%2B-+sqrt%28+-128+%29%29%2F6+

x+=+%284+%2B-+sqrt%28+-1%2A2%2A64+%29%29%2F6+

x+=+%284+%2B-+8sqrt%282%29%2Ai%29%2F6+ ...simplify

x+=+%282+%2B-+4sqrt%282%29%2Ai%29%2F3+

x+=+%282%2F3+%2B-+4sqrt%282%29%2Ai%2F3%29+


solutions:
x+=+%282+%2B+4sqrt%282%29%2Ai%29%2F3+ =>x+=+2%2F3+%2B+4sqrt%282%29%2Ai%2F3+

x+=+%282+-+4sqrt%282%29%2Ai%29%2F3+ =>x+=+2%2F3-+4sqrt%282%29%2Ai%2F3+