Question

if α & β are roots of 5x^2 - 6x + 3= 0 form a quadratic equation whose roots are α^3β ,αβ^3.​

Answer 1

Answer:

 625x² - 90x + 81 = 0

Step-by-step explanation:

From the coefficients of 5x² - 6x + 3, we have

  α + β = 6/5    and    αβ = 3/5.

For the new quadratic, the sum of the roots will be

  α³β + αβ³ = αβ ( α² + β² )

                   = αβ ( ( α + β )² - 2αβ )

                   = 3/5 × ( (6/5)² - 2×3/5 )

                   = 3/5 × 6/5 × 1/5

                   = 18 / 125

                   = 90 / 625

and the product of the roots will be

  α³β × αβ³ = (αβ)⁴ = (3/5)⁴ = 81 / 625.

So a suitable quadratic equation is

 625x² - 90x + 81 = 0

Hope this helps!