Question

If alpha and bita are zeroes of the polynomial x²-5x+3 find the value alpha³ +bita³​

Answer 1

Step-by-step explanation:

Given:

x2+5x+3=0x2+5x+3=0

The roots of the equation are :α:αandββ

α+β=−baα+β=−ba

⟹α+β=−5……..(1)⟹α+β=−5……..(1)

α∗β=caα∗β=ca

⟹α∗β=3……….(2)⟹α∗β=3……….(2)

(α+β)2=α2+β2+2α∗β(α+β)2=α2+β2+2α∗β

⟹(−5)2=α2+β2+2∗3[See(1) and (2)]⟹(−5)2=α2+β2+2∗3[See(1) and (2)]

⟹α2+β2=25–6⟹α2+β2=25–6

⟹α2+β2=19………(3)⟹α2+β2=19………(3)

Now,(α−β)2=α2+β2–2α⋅βNow,(α−β)2=α2+β2–2α⋅β

⟹(α−β)2=19–6