Question
Download Solution PDFIf one root of the equation exceeds the other by \(2\sqrt{3}\) then which one of the following is a value of k?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The quadratic equation is x2 - kx + k = 0.
One root exceeds the other by 2√3.
⇒ α - β = 2√3.
Also,
Sum of roots: α + β = k
Product of roots: α × β = k
Calculation:
We know the following identity
\((\alpha + \beta )^2 = (\alpha - \beta)^2 - 4\alpha\beta \)
⇒ k2 = (2√3)2 - 4k
⇒ k2 - 12 - 4k = 0
⇒ k2 - 6k + 2k -12 = 0
⇒ k(k - 6) + 2 ( k - 6) = 0
⇒ (k - 6) (k + 2) = 0
⇒ k = 6 and k = -2
Thus, the possible values of k are 6 and -2
Hence, the correct answer is Option 2.
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