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DaveC426913

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I'm helping edit a math textbook and have been asked to provide the answer for this:

Factor to find the value of b and c in the trinomial:

-0.5x2 + x -1= -0.5 (x2 - bx + c)

Here is what I've done:

-0.5x^2 + x -1= -0.5 (x^2 - bx + c)

-0.5x^2 + x -1= x^2 + .5bx - .5c

-0.5x^2 + x -1= x^2 + .5bx - .5c

x -1= 1.5x^2 + .5bx - .5c

-1 = 1.5x^2 - .5bx - .5c

1.5x^2 - .5bx - .5c +1 = 0

or, in latex:

[tex]-0.5x^2 + x -1= -0.5 (x^2 - bx + c)[/tex]

[tex]-0.5x^2 + x -1= x^2 + .5bx - .5c[/tex]

[tex]-0.5x^2 + x -1= x^2 + .5bx - .5c[/tex]

[tex]x -1= 1.5x^2 + .5bx - .5c[/tex]

[tex]-1 = 1.5x^2 - .5bx - .5c[/tex]

[tex]1.5x^2 - .5bx - .5c +1 = 0[/tex]

Ultimately, I'm going to end up with factors of the form (ax^2+b+?)(x^2+c+?) ? Oh shoot . I don't know what I'm supposed to end up with. The question wants values for b and c. It's been 25 years!

So, am I then supposed to use trial and error?

if b=1, c=3

1.5x^2 - .5bx - .5c +1 = 0

then 1.5x^2 – .5x - .5 = 0

So (1.5x + .5)(x - 1) (This isn't quite right, since it actually makes 1.5x2 – x -1=0, but I think I'm close.)

Even if I get the right answer, I'll need to hsow my work, I can't tellt he students to guess can I?

Factor to find the value of b and c in the trinomial:

-0.5x2 + x -1= -0.5 (x2 - bx + c)

Here is what I've done:

-0.5x^2 + x -1= -0.5 (x^2 - bx + c)

-0.5x^2 + x -1= x^2 + .5bx - .5c

-0.5x^2 + x -1= x^2 + .5bx - .5c

x -1= 1.5x^2 + .5bx - .5c

-1 = 1.5x^2 - .5bx - .5c

1.5x^2 - .5bx - .5c +1 = 0

or, in latex:

[tex]-0.5x^2 + x -1= -0.5 (x^2 - bx + c)[/tex]

[tex]-0.5x^2 + x -1= x^2 + .5bx - .5c[/tex]

[tex]-0.5x^2 + x -1= x^2 + .5bx - .5c[/tex]

[tex]x -1= 1.5x^2 + .5bx - .5c[/tex]

[tex]-1 = 1.5x^2 - .5bx - .5c[/tex]

[tex]1.5x^2 - .5bx - .5c +1 = 0[/tex]

Ultimately, I'm going to end up with factors of the form (ax^2+b+?)(x^2+c+?) ? Oh shoot . I don't know what I'm supposed to end up with. The question wants values for b and c. It's been 25 years!

So, am I then supposed to use trial and error?

if b=1, c=3

1.5x^2 - .5bx - .5c +1 = 0

then 1.5x^2 – .5x - .5 = 0

So (1.5x + .5)(x - 1) (This isn't quite right, since it actually makes 1.5x2 – x -1=0, but I think I'm close.)

Even if I get the right answer, I'll need to hsow my work, I can't tellt he students to guess can I?

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