Question

4,44,48,416,………up to ∞ are roots of the equation

• A. (A) x2 - 4 = 0
• B. (B) x2 - 4x + 6 = 0
• C. (C) x2 - 5x + 4 = 0
• D. (D) x2 - 3x + 2 = 0

Answer 1

Answer: (C)

(C) x2 - 5x + 4 = 0

Answer 2

Explanation:
41/2,41/4,41/8,41/16,… are given roots, thenSum of roots=41/2+41/4+41/8+…=5Product of roots=41/2⋅41/4⋅41/8…=41/2+1/4+1/8+…=41/21−1/2=4∴ Required equation is x2−( sum of roots )x+( product of roots )=0⇒x2−5x+4=0