Question
Question: If roots of the equation x<sup>3</sup> – 12x<sup>2</sup> + kx –28 = 0 are in A.P. then k is:...
If roots of the equation x3 – 12x2 + kx –28 = 0 are in A.P. then k is:
A
29
B
39
C
34
D
None of these
Answer
39
Explanation
Solution
Let roots are a – d, a, a + d
Using theory of equation
a – d + a + a + d = 12
Ž a = 4 …(1)
a (a –d) + a(a + d) + (a – d) (a + d) = k …(2)
a (a –d) (a + d) = 28 …(3)
from (1) and (3)
d2 = 9 i.e. d = ± 3 using in eq. (2) and get k.