CAT 2003 - Retake — QA Question 22
Higher Degree PolynomialsEasy
The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is:
Answer & solution
Correct answer: 0
0
- B
1
- C
2
- D
3
Solution
x3 + 3x2 + 4x + 5 = 0 ... (i)
x3 + 2x2 + 7x + 3 = 0 ... (ii)
Equating equations (i) and (ii), we get,
x2 – 3x + 2 = 0
∴ (x – 1)(x – 2) = 0
∴ x = 1 or x = 2
Since both x = 1 and x = 2, do not satisfy either (i) or (ii), there exists no common roots for equations (i) and (ii).
Hence, option (a).