JEE Advanced Maths: Quadratic and Cubic Equations questions with solutions

Q1. Let a, b and c be the roots of 2x³ + x² + x + 1 = 0. Find (i) a + b + c and (ii) a*b*c.

1. (i) -1/2 and (ii) -1/2
2. (i) -1/2 and (ii) 1/2
3. (i) 1/2 and (ii) -1/2
4. (i) -1 and (ii) -1

Answer: (i) -1/2 and (ii) -1/2

For 2x³ + x² + x + 1 = 0: A=2, B=1, C=1, D=1. Sum a+b+c = -B/A = -1/2. Product a*b*c = -D/A = -1/2.