AP EAMCET · Maths · Quadratic Equation
The value of \(k\) for which the equation \(x^2-3 x+k=0\) has at least one real root in \([0,1]\) is
- A \(\frac{5}{2}\)
- B \(\frac{7}{6}\)
- C 3
- D \(\frac{20}{7}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{6}\)
Step-by-step Solution
Detailed explanation
For the equation \(x^2-3x+k=0\) to have at least one real root in \([0,1]\), since the axis of symmetry is \(x=\frac{3}{2} > 1\), the smaller root \(x = \frac{3-\sqrt{9-4k}}{2}\) must lie in \([0,1]\). For real roots: \(9-4k \ge 0 \implies k \le \frac{9}{4}\). Condition…
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