Question

if alpha and beta are the zeros of the quadratic polynomial x ^2-7x+10, find the value of (Alpha ^3+Beta ^3).I will surely mark u as brainliest .plss ans it

Answer 1

Hi friend, Here is the required answer :-
To find the zeroes of the polynomial,
x²-7x+10=0
x²-5x-2x+10=0
x(x-5)-2(x-5)=0
(x-2)(x-5)=0
So, x= 2, x=5.
So, alpha =2, beta= 5.
(alpha) ³+(beta)³=2³+5³=8+125=133.

Hope this helps you....
PLEASE MARK AS BRAINLIEST ANSWER!

Answer 2

Given:
Quadratic Polynomial = x²-7x+10 
α and β are the zeros of the quadratic polynomial x²-7x+10 

To find: 
the value of (α³+β³) 

Solution: 
To find the zeros of the polynomial we can use 3 methods but I'm currently using the factorization method. 

⇒ x²-7x+10 = 0

⇒ x²-5x-2x+10 = 0

⇒ x(x-5)-2(x-5) = 0 

⇒ (x-5) (x-2) = 0 

⇒ (x-5) = 0  (or)  (x-2) = 0 

⇒ x = 5    (or)   x = 2 

∴ α=5 & β=2 

(α³+β³) = (5³+2³) 
(α³+β³) = (125+8) 
(α³+β³) = (133)

∴ (α³+β³) = (133)