Question

if alpha and beta are zeros of 3x2 -4x+1 find polynomial whose zeros are alpha square/beta and beta square/alpha

Answer 1

Hey there!

For the quadratic equation with roots, α ,β
Sum of roots = 4/3
Product of roots = 1/3 .

Now, The quadratic equation with roots α²/β ,
β²/ α

Now,
Sum of roots = α²/β + β²/ α = α³+β³/αβ
= (α + β)³-3αβ(α+β)/αβ
= (4/3)³-3(1/3)(4/3) / 1/3
= 64/27 - 4/3 / 1/3
= 64/27-36/27 / 1/3
= 28/27 * 3/1
= 28/9


Product of roots = (α²/β * β²/ α) = (αβ ) = 1/3 .

The quadratic equation with required roots = x²-28/9x + 1/3 = 9(x² - 28/8x+1/3) = 9x² - 28x + 3

Hope helped

Answer 2

Answer:

Plz find the attachment.

This answer is absolutely right.

Same question in ulike.