If α,β and γ are the roots of the equation x3-8x+8=0, then ∑α2 and ∑1αβ are respectively
0 and -16
16 and 18
-16 and 0
16 and 0
Explanation for the correct option:
Find the value of ∑α2 and ∑1αβ:
Given, α,β and γ are the roots of the equation x3-8x+8=0
⇒∑α=0,∑ɑβ=–8,ɑβɣ=–8
As we know,
∑ɑ2=(α+β+γ)2–2∑ɑβ=0–2(-8)=16
and
∑1ɑβ=∑ɑɑβɣ=0 ∵∑α=0
∴The required values are 16 and 0
Hence, Option ‘D’ is Correct.
If α,β and γ are the roots of the equation x3+3x+2=0 , Find the equation whose roots are (α−β)(α−β),(β−γ)(β−α),(γ−α)(γ−β).