Question
Question: If the roots of the equation x<sup>3</sup> – 12x<sup>2</sup> + 39x –28 = 0 are in A.P. then their co...
If the roots of the equation x3 – 12x2 + 39x –28 = 0 are in A.P. then their common difference is
A
± 3
B
±4
C
±5
D
None of these
Answer
± 3
Explanation
Solution
Sum of 3 numbers in A.P.
Ž 3a = 12 Ž a = 4 is a root
x3 –12x2 + 39x –28 = 0
Ž (x – 4) (x2 – 8x + 7) = 0
Ž (x –1) (x –4) (x – 7) = 0
Ž x = 1, 4, 7 or 7, 4, 1
so d = ± 3