Question

If α and β are the zeroes of the polynomial p(x) = 4x2
- 5x - 1, then find the value of
α
3
β+β3α.

Answer 1

$\frac{ - 33}{64} is \: the \: answer$

Step-by-step explanation:

=====================================

See The Attachment My Friend....

=====================================

Answer 2

Answer:

__________________________________

p(x) = 4x² - 5x - 1

Here, a = 4

b = -5 and c = -1

Sum of zeroes

α + β = -b/a

= -(-5)/4 = 5/4

Product of zeroes

αβ = c/a = -1/4

Now,

α³β + β³α

= αβ(α³+β³)

= αβ[(α+β)² - 2αβ]

(since a²+b² = (a+b)² - 2ab)

(substituting α+β = 5/4 and αβ = -1/4)

= -1/4 [(5/4)² - 2(-1/4)]

= -1/4[25/16 + 2/4]

= -1/4 × 33/16

= -33/64

Therefore α³β + β³α = -33/64.

________________________________________________________________________