Question

i) If the sum of the roots of the quadratic equation
ax² + bx + c = 0 is equal to the sum of the
squares of their reciprocals show that bc²,ca²,ab² are in A.P.​

Answer 1

Answer:

plzzz mark me as a brainliest

Answer 2

bc² , ca²  & ab² are in AP If the sum of roots = sum of squares of their reciprocals

Step-by-step explanation:

ax² + bx + c = 0

let say α , β  are the roots

then

α + β   =  1/α²  + 1/β²

LHS =

α + β  

= - b/a

RHS

= 1/α²  + 1/β²  

= (β²   + α²)/α²β²

= ((α + β)² - 2αβ)/α²β²

= ((α + β)² - 2αβ)/(αβ)²

αβ = c/a

= ( (-b/a)² - 2(c/a) ) /(c/a)²

=  (b² - 2ac)/c²

- b/a  = (b² - 2ac)/c²

=> -bc²  = ab²  - 2a²c

=> 2a²c = ab² + bc²

=> 2ca² = bc² + ab²

hence  bc² , ca²  & ab² are in AP

Learn more:

If the sum of the roots of the quadratic equation

https://brainly.in/question/1145904

if alpha and beta are the roots of the quadratic equation 3 X square ...

https://brainly.in/question/14253348