Quadratics

[Probability]

Please accept my appolgies if I posted this in the wrong section?

I want to solve;

x² - 4x - 3 = 0

I could use the formula and conclude the answers as;

x = 2 + or - sqrt 7

Now my algebra is still in the learning curve and factorising is still also a learning curve. I use BODMAS to help me get the order of events correctly done, but BODMAS does have some equal priorities in it and this is just giving me slight confusion in using it for the order of events.

So I will explain this way to see if anyone can say yes you are making a mistake or your OK?

x² - 4x - 3 = 0

(x - 1)(x + 3) (I HAVE JUST REALISED THESE FACTORS ARE INCORRECT)

Using FOIL I get;

x² - 3x - x - 3

x² - 4x - 3 = 0

So I have factors of

x = 1 and x = - 3

THIS IS THE PROBLEM AREA

Using x = - 3

x² - 4x - 3 = 0

- 3 - 4( - 3) - 3 = 9 + 12 - 3 = Now addition comes before subtraction but the priorities are equal, so

is it

9 + 12 = 21 - 3 = 18, which is the wrong answer, although BODMAS recommends starting from left to right to solve problems, or is it OK to do this;

x² - 4x - 3 = 0

- 3 - 4( - 3) - 3 = 9 - 12 - 3 = 0

I am a bit confused although the factors do seen to work the BODMAS priority is not fully understood by me?

Thanks

Probability

 

[Deleted member 4993]

Please accept my appolgies if I posted this in the wrong section?

I want to solve;

x² - 4x - 3 = 0

I could use the formula and conclude the answers as;

x = 2 + or - sqrt 7

Now my algebra is still in the learning curve and factorising is still also a learning curve. I use BODMAS to help me get the order of events correctly done, but BODMAS does have some equal priorities in it and this is just giving me slight confusion in using it for the order of events.

So I will explain this way to see if anyone can say yes you are making a mistake or your OK?

x² - 4x - 3 = 0

(x - 1)(x + 3) (I HAVE JUST REALISED THESE FACTORS ARE INCORRECT)

Using FOIL I get;

x² - 3x - x - 3 .............. → .......................... This is incorrect. It should be x² + 3x - x - 3 → x² + 2x - 3

x² - 4x - 3 = 0

So I have factors of

x = 1 and x = - 3

THIS IS THE PROBLEM AREA

Using x = - 3

x² - 4x - 3 = 0

- 3 - 4( - 3) - 3 = 9 + 12 - 3 = Now addition comes before subtraction but the priorities are equal, so

is it

9 + 12 = 21 - 3 = 18, which is the wrong answer, although BODMAS recommends starting from left to right to solve problems, or is it OK to do this;

x² - 4x - 3 = 0

- 3 - 4( - 3) - 3 = 9 - 12 - 3 = 0

I am a bit confused although the factors do seen to work the BODMAS priority is not fully understood by me?

Thanks

Probability

.

 

[Probability]

.

I agree and the factors are also incorrect.

 

[JeffM]

Please accept my appolgies if I posted this in the wrong section?

I want to solve;

x² - 4x - 3 = 0

I could use the formula and conclude the answers as;

x = 2 + or - sqrt 7 Correct

Now my algebra is still in the learning curve and factorising is still also a learning curve. I use BODMAS to help me get the order of events correctly done, but BODMAS does have some equal priorities in it (No, there is no ambiguity: you go left to right within BODMAS) and this is just giving me slight confusion in using it for the order of events.

So I will explain this way to see if anyone can say yes you are making a mistake or your OK?

x² - 4x - 3 = 0

(x - 1)(x + 3) (I HAVE JUST REALISED THESE FACTORS ARE INCORRECT)

Using FOIL I get;

x² - 3x - x - 3

x² - 4x - 3 = 0

So I have factors (you mean roots or zeroes) of

x = 1 and x = - 3 But this too is incorrect because it is derived from an incorrect factorization

THIS IS THE PROBLEM AREA

Using x = - 3

x² - 4x - 3 = 0

(-3)² - 4( - 3) - 3 = 9 + 12 - 3 = Now addition comes before subtraction but the priorities are equal, so

is it

(9 + 12) - 3 = 21 - 3 = 18 = 9 + 9 = 9 + (12 - 3), which is the SAME wrong answer whichever order you choose, although BODMAS recommends starting from left to right to solve problems, or is it OK to do this;

x² - 4x - 3 = 0

(- 3)² - 4( - 3) - 3 = 9 - 12 - 3 = 0 BUT THIS IS ALSO AN ERROR - 4(- 3) = +12 AND 9 - 12 - 3 = - 3 - 3 = - 6

I am a bit confused although the factors do seen to work the BODMAS priority is not fully understood by me?

Thanks

Probability

The problem is not BODMAS, but your multiple errors.

 

[HallsofIvy]

You should have realized, when you saw that this equation did NOT have rational roots, that it could NOT have factors with integer coefficients.