JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The smallest positive integral value of \( a \), for which all the roots of \( x^{4}-ax^{2}+9=0 \) are real and distinct, is equal to
- A 9
- B 3
- C 4
- D 7
Answer & Solution
Correct Answer
(D) 7
Step-by-step Solution
Detailed explanation
\(x^4-a x^2+9=0 \quad\ldots(1)\) \(\text {let } x^2=t\) \(t^2-a t+9= \quad\ldots(2)\) for roots of equation (1) to be real & distinct roots of equation (2) must be positive & distinct. (i) \(D>0 \Rightarrow a^2-36>0 \Rightarrow a \in(-\infty,-6) \cup(6, \infty)\) (ii)…
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