Quadratic Eqaution & Factorizing x^2 - 2x - 6 = 0
- Thread starter Thinker
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It it important to understand HOW you arive at the quadratic formula, by completing the square. You should do a little research and then come back for help if you need it, showing the steps you have taken, first, on your own.
start here how to use the quadform: http://www.purplemath.com/modules/quadform.htm
how to arive at the quadratic formula, by completing the square:
http://www.purplemath.com/modules/sqrquad2.htm#formula
Impress your teacher, by showing him/her that you not only know how to plug in values for the quadratic formula, identifying a,b and c; but you know the steps to get there.
Show your work if you need help.
start here how to use the quadform: http://www.purplemath.com/modules/quadform.htm
how to arive at the quadratic formula, by completing the square:
http://www.purplemath.com/modules/sqrquad2.htm#formula
Impress your teacher, by showing him/her that you not only know how to plug in values for the quadratic formula, identifying a,b and c; but you know the steps to get there.
Show your work if you need help.
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- Feb 4, 2004
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If the instruction you're receiving in class and from your text is as poor as what is displayed here, it's no wonder you're confused. The exercise in (a) is an equation, not an expression; expressions cannot be "solved". And the exercise in (b) is an expression, not an equation; equations do not get "factored".
Also, what on earth do they mean by "evaluating the function of the equation"? Are they maybe asking you to find the zeroes of the related function f(x) = x<sup>2</sup> - 2x - 6...?
*sigh*
Eliz.
arthur ohlsten
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- Feb 20, 2005
- Messages
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x^2-2x-6=0
can this be factored with integers?
facxtors of x^2 coefficient 1........1,1
factors of 6................................1,6;2,3
we want a set whose difference of cross products =2 there are none
how do we factor ax^2+bx+c =0?
divide by a
x^2+b/a x + c/a=0 rewrite
[x^2+b/a x + ] + c/a =0
complete the square
[x^2+b/a x + [b/2a]^2 ] -[b/2a]^2 +c/a=0
[x+b/2a]^2=b^2/(4a^2) -c/a
place right side of = sign over common denominator
[x+b/[2a] ]^2= [b^2 -4ac] /[4a^2]
take square root
x+b/2a= +/- [b^2-4ac]^1/2 /2a
x=-b +/-[ b^2-4ac]^1/2 all over 2a
x^2-2x-6=0
a=1
b=-2
c=-6
x=2+/-[4-4[1][-6]]^1/2 all over 2
x=2+/-[4+24] all over 2
x=2 +/- 1/2 [28]^1/2
x=2+/- 1/2 [2*2*7]^1/2
x=2 +/- sqrt7
x=2+sqrt7 answer
x=2-sqrt7 answer
can this be factored with integers?
facxtors of x^2 coefficient 1........1,1
factors of 6................................1,6;2,3
we want a set whose difference of cross products =2 there are none
how do we factor ax^2+bx+c =0?
divide by a
x^2+b/a x + c/a=0 rewrite
[x^2+b/a x + ] + c/a =0
complete the square
[x^2+b/a x + [b/2a]^2 ] -[b/2a]^2 +c/a=0
[x+b/2a]^2=b^2/(4a^2) -c/a
place right side of = sign over common denominator
[x+b/[2a] ]^2= [b^2 -4ac] /[4a^2]
take square root
x+b/2a= +/- [b^2-4ac]^1/2 /2a
x=-b +/-[ b^2-4ac]^1/2 all over 2a
x^2-2x-6=0
a=1
b=-2
c=-6
x=2+/-[4-4[1][-6]]^1/2 all over 2
x=2+/-[4+24] all over 2
x=2 +/- 1/2 [28]^1/2
x=2+/- 1/2 [2*2*7]^1/2
x=2 +/- sqrt7
x=2+sqrt7 answer
x=2-sqrt7 answer
Hey arthur ohlsten thank you very much explaining and finding out the answer for me.arthur ohlsten said:
I needed to get that question right just to get a pass on my assignment, thank you ever so much.
when they say "evaluating the function of the equation", to get your answer and get the zero.
Thanks for the help mate!
arthur ohlsten
Full Member
- Joined
- Feb 20, 2005
- Messages
- 852
I didn't do b)
b)
x^2-4x-32
factor
factors of 1[x^2 term]=1,1
factors of 32 [constant term)=1,32 ; 2,16 ; 4;8
we want a set whose difference (- sign for constant term) equals 4 [ x coefficient)
1,1 ; 4,8 does it
[x-8][x+4]=0
x=8 OR x= -4 answer
You should use the quadratic equation and get the same answer
Arthur
b)
x^2-4x-32
factor
factors of 1[x^2 term]=1,1
factors of 32 [constant term)=1,32 ; 2,16 ; 4;8
we want a set whose difference (- sign for constant term) equals 4 [ x coefficient)
1,1 ; 4,8 does it
[x-8][x+4]=0
x=8 OR x= -4 answer
You should use the quadratic equation and get the same answer
Arthur