If the roots of the equation a(b – c)x2 +b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 2/b = (1/ a) + (1/ c)
a(b - c)x2 + b(c - a)x + c(a - b) = 0
On putting x = 1, the equation is satisfied α = 1
Now, since it is given that both roots are equal
so, β = 1
α + β = 2
-b(c - a)/[a(b - c)] = 2
-bc + ab = 2ab - 2ac
2ac = ab + bc
Dividing both sides by abc
2/b = (1/a) + (1/c)