Question

if the sum of roots of ...​

Answer 1

Answer:

2a²c = cb²+b²a

Solution :

• Sum of roots = -b/a--(1)

• product of roots = c/a

• Sum of squares of reciprocals = 1/@² + 1/ß²

• 1/@²+1/ß² = @²+ß²/(@ß)²

• (@+ß)²-2@ß / (@ß)²

• (-b/a)²-2(c/a) / (c/a)²

• b²/a² - 2ac/a² / c²/a²

• 1/@²+1/ß² = b²-2ac/c² ---(2)

Given , sum of roots = Sum of squares of reciprocals

• -b/a = b²-2ac / c²

• -bc² = ab² - 2a²c

• 2a²c = ab² + bc²

• 2a²c = c²b + b²a

Hence proved 2a²c = c²b + b²a if sum of roots = Sum of squares of reciprocals

For more information regarding the sum of roots and product of roots and their proofs reffer the following link

https://brainly.in/question/21061855