Question

if the root of the equation(a -b )x² + (b -c )x + (c - a)= 0 are equal, prove that 2a = b + c.

Answer 1

☆hey Megha!!!☆

here is your answer ☞
→_→→_→→_→→_→

given equation

(a-b)x²+(b-c)x+(c-a) = 0 ____(1)

the roots of the given equation are equal

then

we know that

D = 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+c²-4ab+2bc-4ac= 0

{(a+b+c)² = a²+b²+c²+2ab+2bc+2ac}

so

=> (-2a+b+c)² = 0

=> -2a + b + c = 0

=> 2a = b+c _______proved


hope it will help you ☺☺☺

Devil_king ▄︻̷̿┻̿═━一