SOLUTION: Consider the following. f(x)=1/2x^2+3/2x-1/2 (a) Find all the real zeros of the polynomial function.

Algebra ->  Equations -> SOLUTION: Consider the following. f(x)=1/2x^2+3/2x-1/2 (a) Find all the real zeros of the polynomial function.       Log On


   

Question 675635: Consider the following.
f(x)=1/2x^2+3/2x-1/2

(a) Find all the real zeros of the polynomial function.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = %281%2F2%29x%5E2+%2B+%283%2F2%29x+-+%281%2F2%29
0+=+%281%2F2%29x%5E2+%2B+%283%2F2%29x+-+%281%2F2%29
...
Multiply both sides of the equation by 2
0+=+x%5E2+%2B+3x+-+1
...
Complete the square
x%5E2+%2B+3x+%2B+2.25+=+1+%2B+2.25
%28x%2B1.5%29%5E2+=+3.25
sqrt%28x%2B1.5%29%5E2 = +/- sqrt%283.25%29
...
x+1.5 = +/- sqrt%283.25%29
x = -1.5 +/- sqrt%283.25%29
...
x = -1.5 + 1.8 = highlight_green%28.3%29
x = -1.5 - 1.8 = highlight_green%28-3.3%29
...
using the quadratic formula
x = %28-%283%2F2%29+%2B-+sqrt%28%283%2F2%29%5E2-4%281%2F2%29%28-1%2F2%29%29%29%2F2%281%2F2%29
...
x = %28-%283%2F2%29+%2B-+sqrt%28%289%2F4%29-%28-2%2F2%29%29%29%2F%282%2F2%29
...
x = %28-3%2F2%29+%2B-+sqrt%28%289%2F4%29%2B1%29%29%2F1
...
x = %28-3%2F2%29+%2B-+sqrt%28%289%2F4%29%2B1%284%2F4%29%29
...
x = %28-3%2F2%29+%2B-+sqrt%2813%2F4%29
...
x = %28-3%2F2%29+%2B-+%28sqrt%2813%29%2F2%29
...
x = %28%28-3%29%2B-+sqrt%2813%29%29%2F2
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