Question

If α and β are the zeroes of the quadratic polynomial
f(x) = 3x²- 5x-2, then evaluate α³+β³​

Answer 1

Answer:

215/27

Step-by-step explanation:

if α and β are zeroes of f(x) = ax^2 + bx + c,

α^3 + β^3 = (α + β)(α^2 - αβ + β^2) = (α + β)[(α + β)^2 - 3αβ].

Plugging in -b/a for α + β and c/a for αβ:

α^3 + β^3 = (-b/a)(b^2/a^2 - 3c/a)

= (-b/a)(b^2 - 3ac)/a^2

= b(3ac - b^2)/a^3.

∴ from the above =215/ 27

Answer 2

Answer:

Step-by-step explanation:

alfa + beta = -b/a = -(-5)/3 = 5/3

alfa x beta = c/a = (-2)/3    = -2/3

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