SOLUTION: FInd the zeros of f(x)=x2 - 2X - 5

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Question 150922: FInd the zeros of f(x)=x2 - 2X - 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-2x-5=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-2, and c=-5


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-2, and c=-5


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--20+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-5%29 to get -20


x+=+%282+%2B-+sqrt%28+4%2B20+%29%29%2F%282%281%29%29 Rewrite sqrt%284--20%29 as sqrt%284%2B20%29


x+=+%282+%2B-+sqrt%28+24+%29%29%2F%282%281%29%29 Add 4 to 20 to get 24


x+=+%282+%2B-+sqrt%28+24+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%286%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+sqrt%286%29 Reduce.


x+=+1%2Bsqrt%286%29 or x+=+1-sqrt%286%29 Break up the expression.


So our answers are x+=+1%2Bsqrt%286%29 or x+=+1-sqrt%286%29


which approximate to x=3.449 or x=-1.449