Question

05 If α and β are the zeroes of the polynomial p(x)=4x^2-5x-1, then find the value of the following (i) α^2+β^(2 ) (ii) α^3+β^3 (iii) α-β (iv) α^2 β+β^2 α (v) α/β+β/α (vi) α^2/β^2 +β^2/α^2

Answer 1

Answer:

sum of roots = α + β = -b/a = 5/4

product of roots = αβ = c/a = -1/4

(1) α^2+β^ = (α + β)² - 2αβ = (5/4)² +1/2 = 25/16 + 1/2 = 33/16 (Ans)

(2) α^3+β^3 = (α + β)³ -3αβ(α + β) = (5/4)³ +3/4(5/4) = 125/64 + 15/16 = 185/64 (Ans)

Answer 2

Answer:

Step-by-step explanation:

sum of roots = α + β = -b/a = 5/4

product of roots = αβ = c/a = -1/4

(1) α^2+β^ = (α + β)² - 2αβ = (5/4)² +1/2 = 25/16 + 1/2 = 33/16 (Ans)

(2) α^3+β^3 = (α + β)³ -3αβ(α + β) = (5/4)³ +3/4(5/4) = 125/64 + 15/16 = 185/64