Question

if alpha and beta are the roots of the quadratic equation 5x^ - 8x + 3 = 0 then find the quadratic equation whose roots are alpha/ beta and beta/alpha​

Answer 1

Answer:

15x² - 34x + 15 = 0

Step-by-step explanation:

sum of roots = 8/5

product of roots = 3/5

∴ α + β = 8/5

αβ = 3/5

sum of roots of the required equation

= α/β + β/α

= (α²+β²)/(αβ)  

= [ (α+β)² - 2αβ ] / (αβ)

= [ (8/5)² - 2(3/5) ] / (3/5)

= 34/15

product of roots of the required equation

= (α/β) (β/α)

= 1

∴ Required equation:

x² - (sum of roots)x +  (product of roots) = 0

x² - (34/15)x + 1 = 0

15x² - 34x + 15 = 0