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Deffense [45]
2 years ago
15

if the zeroes of the polynomial, p(x)= ax^3 + 3bx^2 + 3cx + d = 0 be alpha - beta, alpha and alpha + beta. Prove that 3abc = a^2

d + 2b^3 ...please do mention step by step...and explain the process​..
Mathematics
1 answer:
swat322 years ago
7 0

Step-by-step explanation:

p(x) = ax³ + 3bx² + 3cx + d

Roots are α−β, α, and α+β.

The sum of the roots of a cubic y = ax³ + bx² + cx + d is -b/a.  Therefore:

α−β + α + α+β = -3b/a

3α = -3b/a

α = -b/a

α is a root, so p(α) = 0.

0 = a(α)³ + 3b(α)² + 3c(α) + d

Substitute α = -b/a:

0 = a(-b/a)³ + 3b(-b/a)² + 3c(-b/a) + d

0 = -(b³/a²) + 3b³/a² − 3bc/a + d

0 = -b³ + 3b³ − 3abc + a²d

0 = 2b³ − 3abc + a²d

3abc = 2b³ + a²d

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Answer:

C.

Step-by-step explanation:

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2 years ago
Describe the transformation that takes f(x)=x+1 to g(x) = -x+4. Will Mark Brainliest.​
lions [1.4K]

Answer:

Reflection across y axis

Translate up by 3 units

Step-by-step explanation:

Given

f(x) = x + 1

g(x) = -x + 4

Required

Describe the transformation from f(x) to g(x)

First, take a reflection of f(x) across the y axis.

So f(x) becomes f(-x)

f(x) = x + 1 when reflected

f(-x) = -x +1

Next, translate f(-x) up by 3 units to give g(x)

g(x) = f(-x) + k

Where

k = 3

f(-x) = -x +1

g(x) = -x + 1 + 3

g(x) = -x + 4

Hence, the transformation from f(x) to g(x) includes:

Reflection across y axis

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6 0
3 years ago
Samantha moved out of her house and sold some tables and chairs. She sold 30 chairs and tables and made a total of 1640. If each
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janice invests a total of 8000 in two different accounts. the first account returns 5%, while the second account returns 8%. if
Zinaida [17]

Answer:

"She invested $2500 in 5% account and $5500 in 8% account"

Step-by-step explanation:

Let the amount invested in 5% account be "x"

So, the amount invested in 8% account would be "8000 - x"

Interest amount is the percentage multiplied by amount invested. So

Interest of 5% account = 5% of x = 0.05x

Interest of 8% account = 8 % of 8000 - x = 0.08(8000 - x)

Total interest is the sum of these 2 expressions that EQUATES to 565 (given). Let's solve for x:

0.05x + 0.08(8000 - x) = 565\\0.05x+640-0.08x=565\\0.03x=75\\x=2500

and thus,

"8000 - x" = 8000 - 2500 = 5500

Hence,

She invested $2500 in 5% account and $5500 in 8% account

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mojhsa [17]

Answer:

5,2

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this is the distance of these points

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