JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
lf \(2 + 3i\) is one of the roots of the equation \(2x^3 -9x^2 + kx- 13 = 0,\) \(k \in R,\) then the real root of this equation
- A exists and is equal to \(-\frac {1}{2}\)
- B exists and is equal to \(\frac {1}{2}\)
- C exists and is equal to \(1.\)
- D does not exist.
Answer & Solution
Correct Answer
(B) exists and is equal to \(\frac {1}{2}\)
Step-by-step Solution
Detailed explanation
\(\alpha=2+3 i ; \beta=2-3 i, \gamma=?\) \(\alpha \beta \gamma=\frac{13}{2}\left[\text { since product of roots }=\frac{d}{a}\right]\) \(\Rightarrow(4+9)=\frac{13}{2} \Rightarrow \gamma=\frac{1}{2}\)
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