Question

If the roots of the equation (a - b) x² + (b-c)x+(c-a)= 0 are
equal then the value of (b + c) is
A. 2a
B. 2bc
C.2c
D. 2ab​

Answer 1

Answer:

2bc

Step-by-step explanation:

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Answer 2

Given:

Roots of the equation (a - b)x² + (b - c)x + (c - a)= 0 are equal

To find:

Value of b + c

Solution:

Comparing the given equation with Ax² + Bx + C = 0

• A = a - b
• B = b - c
• C = c - a

Roots of equation are equal, So Discriminant = 0

B²- 4AC = 0

(b - c)² - 4(a - b)(c - a) = 0

b² + c² - 2bc - 4(ac - a² - bc + ab) = 0

b² + c² - 2bc - 4ac + 4a² + 4bc - 4ab = 0

4a² + b² + c² + 2bc - 4ac - 4ab = 0

It can be written as

(2a)² + (-b) ² + (-c)² + 2(-b)(-c) + 2(2a)(-c) + 2(2a)(-b) = 0

Using algebraic identity x² + y² + z² + 2xy + 2yz + 2zx = ( x + y + z)²

(2a - b - c)² = 0

2a - b - c = 0

2a = b + c

b + c = 2a

Therefore the value of b + c is 2a.