AP EAMCET · Maths · Quadratic Equation
Let \((a-3) x^2+12 x+(a+6)>0, \forall x \in R ~\&~ a \in(\ell, \infty)\). If \(\alpha\) is the least positive integral value of \(a\), then the roots of \((\alpha-3) x^2+12 x+(\ell+2)=0\) are
- A 1,2
- B 2,3
- C \(-1,-2\)
- D \(-2,-3\)
Answer & Solution
Correct Answer
(C) \(-1,-2\)
Step-by-step Solution
Detailed explanation
\(a-3 > 0 \Rightarrow a > 3\) \(12^2 - 4(a-3)(a+6) \(36 - a^2 - 3a + 18 0\) \((a+9)(a-6) > 0 \Rightarrow a \in (-\infty, -9) \cup (6, \infty)\) \(a \in (3, \infty) \cap ((-\infty, -9) \cup (6, \infty)) \Rightarrow a \in (6, \infty)\) \(\ell = 6\)…
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