Question

if alpha, beta are the roots of x^2+ bx + c then find Alpha power 5 + beta power 5​

Answer 1

α⁵+β⁵ = -b⁵ + 5cb³ - 5bc²

Step-by-step explanation:

(α³+β³)(α²+β²) = α⁵+β⁵ + α²β²(α+β)

=>  α⁵+β⁵ = (α³+β³)(α²+β²) - α²β²(α+β)

=> α⁵+β⁵ = (α+β)(α²+β² - αβ)(α²+β²) - (αβ)²(α+β)

=> α⁵+β⁵ = (α+β)(α²+β² - αβ)((α+β)² - 2αβ) - (αβ)²(α+β)

=> α⁵+β⁵ = (α+β)((α+β)²- 3αβ)((α+β)² - 2αβ) - (αβ)²(α+β)

α+β = - b

αβ = c

=>  α⁵+β⁵ = (-b)(b²- 3c)(b² - 2c) - (c)²(-b)

=>  α⁵+β⁵ = (-b) ( (b²- 3c)(b² - 2c) - (c)²)

=>  α⁵+β⁵ = (-b) ( b⁴ - 5cb² + 6c² - c²)

=>  α⁵+β⁵ = (-b) ( b⁴ - 5cb² + 5c²)

=>  α⁵+β⁵ = -b⁵ + 5cb³ - 5bc²

Learn more:

If alpha and beta are the zeros of the polynomial p(x)=x2-5x+2. Find ...

https://brainly.in/question/9703721

. If the zeroes of the cubic polynomial f(x) = kx3 – 8x2 + 5 are alpha ...

https://brainly.in/question/10004198