If - - I -are the roots of the equation x 2- ax - b -0- where a - i -ln i and b - R- then the number of possible pairs of - - is-areA- 0B- 1C- 2D- 4

X^2+ax+b=0 α + β = a1= a a= iπ×ln i = iπ×ln e^iπ/2=12 nbsp; ∴α + β= a= 12 which is not possible. nbsp; Note: the answer will be same if you take nbsp; i= ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

If α, β∈ I +a...

Question

If $α, β \in I^{+}$ are the roots of the equation $x^{2} + a x + b = 0,$ where $a = - \frac{i}{π} \times ln i$ and $b \in R,$ then the number of possible pairs of $(α, β)$ is/are

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Solution

The correct option is A $0$
$x^{2} + a x + b = 0$
$α + β = \frac{- a}{1} = - a$
$a = - \frac{i}{π} \times ln i$
$= - \frac{i}{π} \times ln e^{\frac{i π}{2}} = \frac{1}{2}$
$∴ α + β = - a = \frac{- 1}{2}$ which is not possible.

Note: the answer will be same if you take $i = e^{i (2 n + 1) \frac{π}{2}}$

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If α,β∈I+ are the roots of the equation x2+ax+b=0, where a=−iπ×lni and b∈R, then the number of possible pairs of (α,β) is/are

The correct option is A 0x2+ax+b=0 α+β=−a1=−a a=−iπ×lni =−iπ×lneiπ2=12 ∴α+β=−a=−12 which is not possible. Note: the answer will be same if you take i=ei(2n+1)π2

If $α, β \in I^{+}$ are the roots of the equation $x^{2} + a x + b = 0,$ where $a = - \frac{i}{π} \times ln i$ and $b \in R,$ then the number of possible pairs of $(α, β)$ is/are