16. If a and B are the root of x² + px + 23=0 and a - B = 1 then Find the value of p.
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Step-by-step explanation:
If α,β are the roots of x2−px+q=0, then the product of the roots of the quadratic ... We need to find the product of (α2−β2) and (α3−β3) ... Hence,option 'B' is correct. ... Algebra 1
Answered by
2
Answer:
If α,β are the roots of the equation x
2
−px+q=0,
⇒ sum of the roots =α+β=p ...(1)
Similarly, product of the roots=αβ=q ....(2)
If
β
α
,
α
β
are roots of the a quadratic equation, then the quadratic equation is given by,
(x−
β
α
)(x−
α
β
)=0
⇒x
2
−(
β
α
+
α
β
)x+1=0
⇒αβx
2
−(α
2
+β
2
)x+1=0
⇒αβx
2
−((α+β)
2
−2αβ)x+1=0 ....(3)
Substituting (1),(2) in (3), we get
qx
2
−(p
2
−2q)x+q=0
⇒qx
2
+(2q−p
2
)x+q=0
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