Quadratic Equations
Quadratic Equations
star_batch_jee_advanced_2025
Grade 11
Question:
Consider the equation $x^4 - (k-1)x^2 + (2-k) = 0$. The complete set of possible values of real $k$ for which the equation has 2 distinct real roots is:
$(0, 2)$
$(-\infty, 2\sqrt{2} - 1)$
$(2, \infty)$
$\{2\sqrt{2} - 1\} \cup (2, \infty)$
Step-by-Step Solution
Key Concept: The substitution method combined with graphical analysis reveals how parameter changes alter the number of real roots.
Using the substitution $x^2 = t$ and analyzing the rational function graph from question 16, determine conditions on parameter $k$ for various root configurations in the original quartic equation.
Correct Answer: 4