Question

If a and b are the zeroes of f(x) = x^2-11x +30, the value of a^3 + b^3 is

Answer 1

Answer:

341

Step-by-step explanation:

x^2-11x+3

x=11±1/2

a=5

b=6

a^3+b^3=125+216⇒341

Answer 2

Good Noon

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Here's your answer

f(x) = x²-11x+30

If α and β are the zeroes of the equation f(x) then,

we know that

α+β = -b/a   and

αβ = c/a

In this case,

a = 1

b = -11

c = 30

Hence,

α+β = -(-11)/1 = 11

αβ = 30/1 = 30

α³+β³ = (α+β)(α²-αβ+β²)

α²+β² = (α+β)² - 2αβ

          = (11)² - 2*30

          = 121 - 60

          = 61

Substituting α²+β² = 61

                      αβ  = 30

                      α+β = 11

α³+β³ = (α+β)(α²+β²-αβ)

         = 11(61 - 30)

         = 11 * 31

         = 341

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