If α + 5 i 2 is a root of the equation 2 x 2 - 6 x + k = 0, then the value of k 10 is α , k , ∈ R

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Question: Answered & Verified by Expert

If

\frac{α + 5 i}{2}

is a root of the equation

2 x^{2} - 6 x + k = 0,

then the value of

\frac{k}{10}

is

(α, k, \in R)

MathematicsQuadratic EquationJEE Main

Solution:

2031 Upvotes Verified Answer

The correct answer is: 1.7

\frac{α + 5 i}{2}

is one root
So,

\frac{α - 5 i}{2}

is the other root

\Rightarrow k = \frac{2}{4} (α^{2} + 25)

= \frac{1}{2} (9 + 25) = 17

\Rightarrow \frac{k}{10} = 1.7

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