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