Question

If x^2+bx+a=0 , ax^2+x+b=0 have a common root and the first equation has equal roots then 2a^2+b is

Answer 1

Step-by-step explanation:

Let u be the common root of the two quadratics.

Since x² + bx + a = 0 has equal roots, that is, both of its roots are u, we have

sum of roots = 2u = -b

product of roots = u² = a

Since u is a root of ax² + x + b = 0 we also have

au² + u + b = 0

Multiplying this last equation by 2 gives

2au² + 2u + 2b = 0

Now substituting the values above for 2u and u² gives

2a×a + (-b) + 2b = 0 ⇒ 2a² + b = 0