Question

If x^2 + px + 1 = 0 and (a – b)x^2 + (b – c)x + (c – a) = 0 have both roots common, then what is the form of a, b, c?

(a) a, b, c are in A.P

(b) b, a, c are in A.P

(c) b, a, c are in G.P

(d) b, a, c are in H.P

I had been asked this question by my college professor while I was bunking the class.

Query is from Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

The correct answer is (b) b, a, c are in A.P

To explain I would say: Given, (a – b)x^2 + (b – c)x + (c – a) = 0 and x^2 + px + 1 =0

So, 1 / (a – b) = p / (b – c) = 1 / (c – a)

Equating the above equation, we get,

(b – c) = p(a – b)      and

(b – c) = p(c – a)

So, p(a – b) = p(c – a)

=> a – b = c – a

So, 2a = b + c which means that b, a, c are in A.P.