Question

if α and β are the zeroes of the polynomial x2 – ax + a , then find the value of (i) α 4 − β 4​

Answer 1

Answer:

Step-by-step explanation:

α + β = -b/a = - ( -a)/1 = a

αβ = c/a = a/1 = a.

α⁴ - β⁴ =   (α²   + β²)(α² - β²)

           = (α²   + β²)(α - β) (α + β)

Find values of α²   + β² and α - β

α²   + β² = (α + β)² - 2αβ  = a² - 2a.

(α - β)² = (α + β)² - 4αβ = a² - 4a

=> α - β = ±√(a² - 4a)

Thus

α⁴ - β⁴ = (a² -2a) (a)(√[a²- 4a]) = (a³ - 2a²)(√[a² - 4a])

Answer 2

Answer is in the pic.