Question

If α and β are the two zeroes of the quadratic polynomial 3x2 -5x + 6, find
alpha cube + beta cube
$6( \frac{5}{3} )$
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Answer 1

Answer:

       -145 / 27

Step-by-step explanation:

3x² -5x + 6

a = 3 , b = -5 , c = 6

∝ + β = -b / a = 5 / 3

∝ + β = 5 / 3

∝β = c / a = 6 / 3 = 2

∝β = 2

(∝ + β)² = ∝² + β² + 2∝β = (5 / 3)²

∝² + β² + 4 = 25 / 9

∝² + β² = 25 / 9 -36 / 9

∝² + β² = -11 / 9

∝³ + β³

= (∝ + β) (∝² - ∝β + β²)

= (5 / 3) (∝² + β² - 2)

= (5 / 3) (-11 / 9 - 2)

= (5 / 3) (-29/9)

= -145 / 27