Polynomial question (1 Viewer)

[Aysce]

Question is:

x^2 - 3x + k - 2 = 0

Solve for k, not sure how to do it :/ thanks.

 

[apollo1]

Question is:

x^2 - 3x + k - 2 = 0

Solve for k, not sure how to do it :/ thanks.

im pretty sure you need some other condition like discriminant equal to zero

 

[Parvee]

Your missing information, don't they give the value of one root?

 

[someth1ng]

You can't exactly solve that unless it's asking for something like "values for k that will allow a real x solution".

 

[Alkanes]

Yep what they said. Missing information making it unsolvable.

 

[Aysce]

Crap sorry guys one root is -4.

 

[Amogh]

Sub in -4 and make it equal to 0.
(If y is a root of P(x) then P(y) = 0)

 

[hscishard]

^ that or using sum of roots, the other root = -1. Product of roots is k-2 = -4. k=-2

 

[Aysce]

Says k = -26

 

[SpiralFlex]

Says k = -26

Yes you can use Amogh's way,

 

[hscishard]

^ that or using sum of roots, the other root = -1. Product of roots is k-2 = -4. k=-2

Whoops
Sum of roots = -4 +a = 3, other root = 7. Product of roots = -28 = k-2. Therefore k =-26
Silly mistakes with the minus signs

 

[Aysce]

Thanks man! And the others (;

 

[taeyang]

Just make f(-4) = 0


edit:
fffff didn't see spi.

 

[Aysce]

One other question is:

Two roots of x^3 + mx^2 + 15x - 7 = 0 are equal and rational find m

 

[OldMathsGuy]

Some like to say equal roots rather than saying there is a single root. In other words for equal roots or a single root, the discriminant = 0.
Does that help you work it out?

Best Regards
OldMathsGuy

 

[SpiralFlex]

Some like to say equal roots rather than saying there is a single root. In other words for equal roots or a single root, the discriminant = 0.
Does that help you work it out?

Best Regards
OldMathsGuy

It is a cubic.


Let the roots be




Let's find the sum.




Let's find the sum and product two at a time.




Now finally product,




From




Into






By inspection or factor theorem,



You must state that since, the second brackets gives you an irrational term.




Place into




Now, into

 

[D94]

...should be ...

 

[SpiralFlex]

...should be ...

Sorry, I was still editing it.

 

[Aysce]

In the step " Into (2)", I don't understand why a^2+2a(7/a^2) = 15 turns into a^2 - 15a + 14 =0

 

[OldMathsGuy]

It is a cubic.

Damn my eyes are going. I am getting old!
So yeah... crafting equations from the roots and simultaneously solving them is the way to go.

Best Regards
OldMathsGuy