Question

a−b+c=0a−b+c=0  , then the roots of ax2+bx+c=0,(a≠c)ax2+bx+c=0,(a≠c)  are​

Answer 1

Given : a−b+c=0 , ax2+bx+c=0

To find : Roots

Solution:

ax² + bx + c = 0

Roots are   (- b ± √(b² - 4ac)) / 2a

a−b+c=0

=> a + c = b

Squaring both sides

=> (a + c)² = b²

=> a² + c² + 2ac  = b²

=> a² + c² + 2ac - 4ac  =  b²  - 4ac

=> a² + c²   - 2ac  =  b²  - 4ac

=> (a - c)² = b²  - 4ac

=> a - c = √(b² - 4ac)

Roots are   (- b ± (a-c)) / 2a  

(-b + a - c) / 2a    or  (-b - a + c) /2a

using b = a + c

=> ( -a - c + a - c)/2a  or  ( -a - c - a + c)/2a

=> -c/a   ,  -1

Roots are   - 1  ,  -c/a  

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