Question

If  x² - 2x + c = 0 and x² - ax + b = 0 have a root in common and the second equation has equal roots, then b + c is equal to

(A)  a

(B)   2a

(C)  3a

(D)  None of these 

Answer 1

Correct option (A) a

x² - ax + b = 0 has equal roots, that is, discriminant is equal to zero.

a² = 4b  .....(i)

x² - 2x + c = 0 have a common root and second equation have identical root.

(b − c)² = (ac − 2b)(2 − a)

⇒ c = a/2 [condition for 1 common root]

Now,

b = c = a/2

So,

b + c = a/2 + a/2 = a