Question

3. If the equations ax2 + bx + c = 0 and cx2 + bx + a = 0 have one root in common, prove that
2 + b + c = 0 or a - b + c = 0.
ADRATIC CLINCTIONS​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

If one root is common so let p is the common root so it satisfies the both eqn

put p in both eqn

ap^2+bp+c=0

cp^2+bp+a=0

ap^2+bp+c= cp^2+bp+a

(a-c)P^2+(c-a)= 0 Take -1 common from (c-a)

(a-c)P^2-(a-c)=0

(a-c)P^2= (a-c)

P^2= 1

P= + or - 1

put p = -1 in eqn 1

we have a-b+c = 0

Proved