AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^2+2 a x+b=0\) are real, distinct and differ atmost by 2 m, then b lies in the interval
- A \(\left(a^2, a^2+m^2\right]\)
- B \(\left(a^2+m^2, a^2\right)\)
- C \(\left[\mathrm{a}^2, \mathrm{a}^2+2 \mathrm{~m}^2\right]\)
- D \(\left[a^2-m^2, a^2\right)\)
Answer & Solution
Correct Answer
(D) \(\left[a^2-m^2, a^2\right)\)
Step-by-step Solution
Detailed explanation
\(D > 0 \Rightarrow (2a)^2 - 4(1)(b) > 0 \Rightarrow 4a^2 - 4b > 0 \Rightarrow b \(|\alpha - \beta| \le 2m \Rightarrow \sqrt{(\alpha+\beta)^2 - 4\alpha\beta} \le 2m\) \(\sqrt{(-2a)^2 - 4b} \le 2m \Rightarrow \sqrt{4a^2 - 4b} \le 2m\)…
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