SOLUTION: solve for the zeros or roots of this polynomial equation g(x)= x^2-6x+8 Please Please explain step by step because I really want to learn how to solve for the zeros of polyno

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve for the zeros or roots of this polynomial equation g(x)= x^2-6x+8 Please Please explain step by step because I really want to learn how to solve for the zeros of polyno      Log On


   

Question 164558: solve for the zeros or roots of this polynomial equation
g(x)= x^2-6x+8
Please Please explain step by step because I really want to learn how to solve for the zeros of polynomial equations. Thank you for any help. Please Help Soon!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The best way to find the roots of a quadratic equation (values that make the ENTIRE equation equal to zero) is to use the quadratic formula.


x%5E2-6x%2B8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-6, and c=8


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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-6, and c=8


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%288%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-32+%29%29%2F%282%281%29%29 Multiply 4%281%29%288%29 to get 32


x+=+%286+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 32 from 36 to get 4


x+=+%286+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


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


x+=+%288%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+4 or x+=+2 Simplify.


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Answer:

So the solutions are x+=+4 or x+=+2