Question

if alpha, beta are the zeroes of quadratic polynomial x2-7x+10,find the value of alpha^3 +beta^3 ​

Answer 1

α and β are the roots of the equation

x² +7x+10=0

therefore, α+β=-7/1=-7

αβ=10/1=10

Now, α³+β³=(α+β)³-3αβ(α+β)

=(-7)²-3.10.(-7)

=49+210

=259

Answer 2

Answer:

ok first i am taking alpha as  'al' and beta as 'be'

Step-by-step explanation:

a = 1,b = -7,c = 10

al + be = -b/a

al + be = 7

al*be = c/a = 10

al^3 + al^3 = (al + be)(al^2 - al*be + be)

                  = 7(al^2 + be^2 - 10)

                  = 7(7^2 - 20 - 10 )     a²+b² = (a+b)² - 2ab

                   = 7(19)

                   = 133

al^3 + al^3  = 133

hope this helps