SOLUTION: Can someone help with the following problem with finding the zeroes? f(x) = 5x^2 - 2x - 1

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Question 275262: Can someone help with the following problem with finding the zeroes?
f(x) = 5x^2 - 2x - 1
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The zeros are the x values that make f%28x%29=0. In other words, they are the x values that satisfy the equation 5x%5E2+-+2x+-+1=0




5x%5E2-2x-1=0 Start with the given equation.


Notice that the quadratic 5x%5E2-2x-1 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-2, and C=-1


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%285%29%28-1%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-2, and C=-1


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%285%29%28-1%29+%29%29%2F%282%285%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%285%29%28-1%29+%29%29%2F%282%285%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--20+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-1%29 to get -20


x+=+%282+%2B-+sqrt%28+4%2B20+%29%29%2F%282%285%29%29 Rewrite sqrt%284--20%29 as sqrt%284%2B20%29


x+=+%282+%2B-+sqrt%28+24+%29%29%2F%282%285%29%29 Add 4 to 20 to get 24


x+=+%282+%2B-+sqrt%28+24+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%282+%2B-+2%2Asqrt%286%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%286%29%29%2F%2810%29 or x+=+%282-2%2Asqrt%286%29%29%2F%2810%29 Break up the expression.


x+=+%281%2Bsqrt%286%29%29%2F%285%29 or x+=+%281-sqrt%286%29%29%2F%285%29 Reduce.


So the solutions are x+=+%281%2Bsqrt%286%29%29%2F%285%29 or x+=+%281-sqrt%286%29%29%2F%285%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Can someone help with the following problem with finding the zeroes?
f(x) = 5x^2 - 2x - 1
-------------------
Use the quadratic formula:
a = 5 ; b = -2 ; c =-1
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x = [2 +- sqrt(4-4*5*-1)]/10
---
x = [2 +- sqrt(24)]/10
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x = [2 +- 2sqrt(6)]/10
---
x = [1 +- sqrt(6)]/5
=============================
Cheers,
Stan H.