If one root is common in equations u^2 ju + i = 0 and u^2 + iu + j = 0 and i \neq j, then which one of the following is correct?

Algebra and Applications Test 3

Question : 11 of 25

Marks: +1, -0

If one root is common in equations

u^2 ju + i = 0

and

u^2 + iu + j = 0

and

i ≠ j

, then which one of the following is correct?

Solution:

Let λ be the common root in equations

u^2 + ju + i + 0

and

u^2 + iu + j + 0

, then

λ^2 + jλ + i = 0

,
and

λ^2 + iλ + j = 0

,
from Eqs. (i) and (ii), we get

⇒λ^2/{j^2-i^2}=λ/{i-j}=1/{i-j}

⇒λ^2=-(i+j)

and

λ=1

⇒1=-(i+j)

⇒i+j=-1

This shows that the both the roots of given equation are always rationals.

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