Question

$p(x) = {3x}^{3} - {5x}^{2} - 11x - 3 \: find \: (1) \frac{1}{ \alpha } + \frac{1}{ \beta } + \frac{1}{ \gamma } \: (2) \: \frac{1}{ \alpha \beta } + \frac{1}{ \beta \gamma } + \frac{1}{ \alpha \gamma } \: (3) \: { \alpha }^{2} \beta \gamma + \alpha { \beta }^{2} \gamma + \alpha \beta { \gamma }^{2}.$
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Answer 1

Answer:

see iam in 6 std so i dont no the asnwer

Step-by-step explanation:

but very sorry

hahahaha

Answer 2

Answer:

Step-by-step explanation:

Comparing the given polynomial with ax³ + bx² + cx + d, we get a = 3, b = – 5, c = –11, d = – 3.

Further p(3) = 3 × 3³ – (5 × 3²) – (11 × 3) – 3 = 81 – 45 – 33 – 3 = 0,

p(–1) = 3 × (–1)³ – 5 × (–1)² – 11 × (–1) – 3 = –3 – 5 + 11 – 3 = 0

p(-1/3) = 3× (-1/3)3 - 5×(-1/3)2 - 11×(-1/3) - 3,

= -1/9-5/9+11/3-3 = 0

Therefore, 3, -1 and -1/3 are the zeroes of 3x³ - 5x² -11x -3

So, we take α = 3, β = -1, γ = -1/3,

Now,

α + β + γ = 5/3 = -(-5)/3 = -b/a,

αβ + βγ + γα = -11/3 = c/a,

αβγ = 1 = -(-3)/3 = -d/a