Question

If α and β are the zeros of the polynomial px² + qx +r then find the value of α³β + β³α
plz answer!!!! ​

Answer 1

Answer:

Hi buddy

Step-by-step explanation:

GIVEN THAT:)

Zeroes of polynomial px²+qx+r=0

alpha and beta are zeroes of polynomial

then,

a+b=-b/a

a+b=-q/p

Again..

ab=c/a

ab=r/p

then,

value of

a³+b³

(a+b)(a²+b²-ab)

(-q/p){(a+b)²-2ab -ab

(-q/p){(-q/p)²-2*r/p -r/p

(-q/p) [(q²/p²-2r/p -r/p

Next step see in attachment

that's all

Answer 2

Answer:

r/p (q²/p² - 2r/p)

Step-by-step explanation:

Given:

• px² + qx +r,  α and β are the zeros

Sum of roots:

• α+β= -q/p

Product of roots:

• α*β =r/p

Solution:

• α³β + β³α=
• αβ(α²+β²)=
• αβ((α+β)²-2αβ)=
• r/p((-q/p)²-2r/p)=

• r/p (q²/p² - 2r/p)

Solved