Answer:
αλ and βλ
Step-by-step explanation:
if alpha beta are the roots of ax² + bx + c = 0, then:
Sum of roots = α + β = -coefficient of x / coefficient of x² = -b/a
product of roots = αβ = Constant / coefficient of x² = c/a
Let x and y be the roots of ax² + bλx + cλ² = 0
Sum of roots = x + y = -coefficient of x / coefficient of x² = -bλ/a
product of roots = xy = Constant / coefficient of x² = cλ²/a
x + y = -bλ/a = λ(α + β) = αλ + βλ
Comparing terms gives:
x = αλ and y= βλ
Therefore the roots of ax² + bλx + cλ² = 0 are αλ and βλ
