Question

What is the sum of the roots of all the quadratic equations that can be formed such that both the roots of the quadratic equation are common with the roots of equation (x-a)(x-b)(x-c)= 0 ?​

Answer 1

Answer:

Step-by-step explanation:

Both the roots of the given equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are always

Answer 2

Given:

(x-a)(x-b)(x -c)= 0

(x – a) (x – b)(x – c) can be as follows:

• (x – a)(x – b) ⇒ Roots are a, b

• (x – b)(x – c) ⇒ Roots are b, c

• (x – c)(x – a) ⇒ Roots are c, a

Now we also have

• (x – a)² ⇒ Roots are a, a

• (x – b)² ⇒ Roots are b, b

• (x – c)² ⇒ Roots are c, c

Adding all these roots, we get 4(a + b + c).

Hence the answer is 4(a + b + c).