Proving Roots: Formula for Solving Quadratic Equations

[lilyhachi]

Summary:: Hi guys, i can't seem to get the correct answer. I'm wondering where did I do wrong. Can someone help me to solve this? I think I need the correct formula to prove the answer :(

Given a root to 𝑥² + 𝑝𝑥 + 𝑞 = 0 is twice the multiple of another. Show that 2𝑝² = 9𝑞. The roots for 𝑥² + 4𝑥 + 𝑘² = −2 − 2𝑘𝑥 − 3𝑘 are not zero and one root is twice the multiple of the other.
Calculate 𝑘.
Ans: 𝑘 = 7

[Moderator's note: moved from a technical forum. Member has been warned to show his efforts next time.]

 

[fresh_42]

Do you know the formula that gives the two roots? You will need it for part a). If you do not know it, then there is a method to get them, namely writing $0=(x^2+px+q)=\left(x+\dfrac{p}{2}\right)^2 + \ldots$

 

[Infrared]

If $r$ and $s$ are the roots, then $rs=q$ and $r+s=-p$. In your case $r=2s$ (without loss of generality). Can you see how to get $2p^2=9q$ from here?

Do you see how this applies to your second problem?

 

[vela]

Summary:: Hi guys, i can't seem to get the correct answer. I'm wondering where did I do wrong.

We can't tell where you went wrong unless you show us what you tried.

 

[Delta2]

If $r$ and $s$ are the roots, then $rs=q$ and $r+s=-q$. In your case $r=2s$ (without loss of generality). Can you see how to get $2p^2=9q$ from here?

Do you see how this applies to your second problem?

I believe you have a typo, it should be $r+s=-p$.

 

[Infrared]

I believe you have a typo, it should be $r+s=-p$.

Yes, of course. Fixed!