JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Consider the quadratic equation \(\left( {c - 5} \right)\,{x^2} - 2cs + \left( {c - 4} \right) = 0\), \(c \ne 5\). Let \(S\) be the set of all integral values of \(c\) for which one root of the equation lies in the interval \((0, 2)\) and its other root lies in the interval \((2, 3)\). Then the number of elements in \(S\) is
- A \(18\)
- B \(12\)
- C \(10\)
- D \(11\)
Answer & Solution
Correct Answer
(D) \(11\)
Step-by-step Solution
Detailed explanation
case \(-1\) \(c-5>0..........(i)\) \(f(0)>0\) \(c-4>0..........(ii)\) \(f(2)<0\) \(4(c-5)-4 c+c-4<0\) \(c<24..........(iii)\) \(f(2)>0\) \(9(c-5)-6 c+c-4>0\) \(4 c-49>0 \Rightarrow c>\frac{49}{4}..........(iv)\) Here \((i)\)…
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