Algebra and Applications Test 3

Question : 14 of 25

Marks: +1, -0

If λ and γ are the roots of the equation

f^ 2 + mf + n = 0

, then what are the roots of the equation

f ^2 - mf + n = 0

Solution:

λ and γ are the roots of the equation

f^2 + mf + n = 0

, then

λ + γ = - m

and

λγ = n

.
Now,

f ^2 - mf + n = 0

⇒ f ^2 +(λ + γ) f + λ γ = 0

⇒ f ^2 + λf + γ f + λ γ = 0

⇒ (λ + γ) (f + γ) = 0

⇒ f = -λ, -γ

This shows that -λ and - γ are the roots of the equation

f ^2 - mf + n = 0

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