Question

If alpha and beta are the roots of equation ax2+bx+c =0 then what are the roots of equation cx2 -bx+a=0

Answer 1

Quadratic equations

• Given: α and β are the roots of the equation ax² + bx + c = 0

• To find: the roots of the equation cx² - bx + a = 0

• Solution.
• Since α and β are the roots of ax² + bx + c = 0, then
• α + β = - b/a .....(i)
• αβ = c/a .....(ii)
• The another equation is cx² - bx + a = 0
• The sum of its roots = b/c
• The product of its roots = a/c
• Now, b/c = (b/a)/(c/a) = - (α + β)/(αβ), by (i)
• = (- 1/α) + (- 1/β)
• Again, a/c = 1/(c/a) = 1/(αβ) = (- 1/α) × (- 1/β)

• Answer. From the above expressions, we can conclude that the roots of the equation cx² - bx + a = 0 are (- 1/α) and (- 1/β).