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JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If both the roots of the quadratic equation \(x^2 - mx + 4 = 0\) are real and distinct and they lie in the interval \([1, 5],\) then \(m\) lies in the interval.
- A \((4,5)\)
- B \((3,4)\)
- C \((5,6)\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
\(x^{2}-m x+4=0\) \(\alpha, \beta \in[1,5]\) \(\text { (1) } \quad \mathrm{D}>0 \Rightarrow \mathrm{m}^{2}-16>0\) \(\Rightarrow \mathrm{m} \in(-\infty,-4) \cup(4, \infty)\) \((2)\) \(\quad f(1) \geq 0 \Rightarrow 5-m \geq 0 \Rightarrow m \in(-\infty, 5]\) \((3)\)…
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