Question

if alpha and beta are the zeros of the quadratic polynomial 4x^2-5x-1 then find the value of alpha^4 beta^2 + alpha^2 beta^4​

Answer 1

Answer:

33/256

Step-by-step explanation:

sum of roots = 5/4

product of roots = -1/4

∴ α + β = 5/4

αβ = -1/4

α⁴β² + α²β⁴

= α²β² (α² + β²)

= α²β² [ (α + β)² - 2αβ ]

= (-1/4)² [ (5/4)² - 2(-1/4) ]

= 33/256