Quadratic Equations
Biquadratic — All Roots Real and Distinct
nta_pyq_2026_jan
Grade 11
Question:
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
Step-by-Step Solution
Key Concept: Let $t=x^2$: $t^2-at+9=0$. For all 4 roots real and distinct: both roots of this quadratic must be positive and distinct. Discriminant $>0$: $a^2-36>0\Rightarrow|a|>6$. Since $a>0$: $a>6$.
Smallest $a=7$.
Correct Answer: 4