Algebra and Applications Test 1

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Question : 37 of 40

Marks: +1, -0

If the roots of the equation

p^2 + p + 1 = 0

are

γ

and

λ

, then

γ+λ=-1\and γλ=1

also the roots of the equation

p^2 + dp + e = 0

are

γ /λ

and

λ/ γ

what is the value of d?

1
2
-1
-2
None of these

Solution:

The roots of the equation

p^2 + p + 1 = 0

are

γ

and

λ

, and the roots of the equation

p^2 + dp + e = 0

are

γ /λ

and

λ/ γ

, then

γ/λ+λ/γ=-d

⇒{(λ^2+γ^2)}/{λγ}=-d

⇒{(λ+γ )^2-2γλ}/{λγ}=-d

⇒{1-2}/1=-d

⇒d=1

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