Algebra
Quadratic Equations, Roots
jee_main_2026_april_4_shift_2
Grade 12
Question:
If the roots of the equation 2x^2 + 5x + k = 0 are reciprocals of each other, and the roots of x^2 - 3x + m = 0 are equal, find the value of k + m.
A. 4
B. 17/4
C. 19/4
D. 21/4
Step-by-Step Solution
Key Concept: Use product of roots = 1 for first equation; discriminant = 0 for second equation.
Step 1: For 2x^2 + 5x + k = 0, product = k/2. Since roots are reciprocals, product = 1 => k/2 = 1 => k = 2. Step 2: For x^2 - 3x + m = 0, equal roots => discriminant = 0 => 9 - 4m = 0 => m = 9/4. Step 3: k + m = 2 + 9/4 = 17/4.
Correct Answer: B
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