Question

If alpha beta are the roots of a x square + bx + c = 0 then the roots of a x square + b λ x + cλ^2 square = λ not equal to zero?

a) λ alpha , λ beta
b) alpha/beta, beta/alpha
c) alpha/ λ , beta/alpha
d) alpha^k, beta^k

Answer 1

αλ and βλ

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