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Quadratic equations

c) α = 5, β =

Use the method shown in the above example to write down the equations whose roots are: (α+β and αβ)

I get...
α+β= 5/4
αβ= -15/4

x2+54x154x=0 x^2 + \frac{5}{4}x - \frac{15}{4}x = 0 ((times by 4 to remove the fractions))
4x2+5x15=0 4x^2 + 5x - 15 = 0

The answer is
4x2 -17x - 15 = 0

What did I do wrong?
Original post by ckfeister
c) α = 5, β =

Use the method shown in the above example to write down the equations whose roots are: (α+β and αβ)

I get...
α+β= 5/4
αβ= -15/4

x2+54x154x=0 x^2 + \frac{5}{4}x - \frac{15}{4}x = 0 ((times by 4 to remove the fractions))
4x2+5x15=0 4x^2 + 5x - 15 = 0

The answer is
4x2 -17x - 15 = 0

What did I do wrong?


α+β54\displaystyle \alpha + \beta \neq \frac{5}{4}
Reply 2
On the next question,
α = -3, β = -4

I get

α+β= -7
αβ= 12


x27x+12=0 x^2 - 7x + 12 = 0


The answer is
x2 + 7x + 12 = 0

What did I do wrong here?
Reply 3
Original post by Mr M
α+β54\displaystyle \alpha + \beta \neq \frac{5}{4}


Nevermind, what about the above?
Original post by ckfeister
How do I do α+β= \alpha + \beta = then?


Type in 534\displaystyle 5-\frac{3}{4} into your calculator?
Reply 5
Original post by Mr M
Type in 534\displaystyle 5-\frac{3}{4} into your calculator?


I noticed after looking at it, I have dyslexic so I can't find these on own for some reason... also what about the other question? I got -7x not +7x (question is above)
Original post by ckfeister
what about the other question? I got -7x not +7x (question is above)


This is the third time you have had the same problem at this final step on different threads so I don't think you are getting it. You always need to change the sign of the sum.

It's because α+β=ba\alpha + \beta = -\frac{b}{a} (note the negative sign).
Reply 7
Original post by Mr M
This is the third time you have had the same problem at this final step on different threads so I don't think you are getting it. You always need to change the sign of the sum.

It's because α+β=ba\alpha + \beta = -\frac{b}{a} (note the negative sign).


So even when shown on α+β \alpha + \beta I still use negative sign? I know ba - \frac{b}{a}
Original post by ckfeister
So even when shown on α+β \alpha + \beta I still use negative sign? I know ba - \frac{b}{a}


To form the quadratic equation do this:

x2x^2 - (sum of roots) x+x + (product of roots) =0=0

This will always give you the right answer.
Reply 9
Original post by Mr M
To form the quadratic equation do this:

x2x^2 - (sum of roots) x+x + (product of roots) =0=0

This will always give you the right answer.


thx
Reply 10
P = FV
Answer is ( 31 )
( -93 1/2 )

How comes I got -42 1/2 on bottom?
(27*-2) + (5*17) = 31
(0*-2) + (-5 1/2*17) = -42.5
??

fp11.jpg
Original post by ckfeister
P = FV
Answer is ( 31 )
( -93 1/2 )

How comes I got -42 1/2 on bottom?
(27*-2) + (5*17) = 31
(0*-2) + (-5 1/2*17) = -42.5
??

fp11.jpg


It's your dyslexia again. You have read a five as a two.
Reply 12
Original post by Mr M
It's your dyslexia again. You have read a five as a two.


Nevermind found it, thx again...
(edited 7 years ago)
Original post by ckfeister
Where?


Negative five point five times seventeen.

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