All categories

3 years ago

From the quadratic equation 3x² + X - 5 = 0, find alpha square plus beta square

Mathematics

1 answer:

timama [110]3 years ago

4 0

Answer:

α² +β² = 3 4/9

Step-by-step explanation:

Assuming α and β are solutions to the equation, it can be factored as ...

(x -α)(x -β) = 0

Expanding this, we get ...

x² -(α +β)x +αβ = 0

Dividing the original equation by 3, we find ...

x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3

We know that the square (α+β)² can be expanded to ...

(α +β)² = α² +β² +2αβ

α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ

Substituting the values for (α+β) and αβ, we find the desired expression is ...

α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9

α² +β² = 3 4/9

You might be interested in

How do animals breakedown rocks.

Hoochie [10]

Answer:

A,B

Step-by-step explanation:

It could be A or B because them stepping on a rock could cause the rock to crack and another could come along and do the same thing and the rock would eventually break.

4 0

3 years ago

Read 2 more answers

Kim and Melody are selling popcorn buckets for a school fundraiser. Customers can buy small buckets or large buckets. Kim sold 3

Papessa [141]

Answer:

The cost of

A small bucket = x = $8

A Larger bucket = y = $13

Step-by-step explanation:

Let the cost of

A small bucket = x

A Larger bucket = y

Kim sold 3 small buckets and 14 large buckets of popcorn for a total of $206.

3x + 14y = 206... Equation 1

Melody sold 11 small buckets and 11 large buckets of popcorn for a total of $231.

11x + 11y = 231.... Equation 2

What is the cost for a small bucket and a large bucket of popcorn?

3x + 14y = 206... Equation 1

11x + 11y = 231 ....... Equation 2

We solve using Elimination method

Multiply Equation 1 by 11 and Equation 2 by 3 to Eliminate x

33x + 154y = 2266.... Equation 3

33x + 33y = 693....... Equation 4

We subtract Equation 4 from Equation 3

121y = 1573

y = 1573/121

y = $13

Solving for x

3x + 14y = 206... Equation 1

3x + 14 × 13 = 206

3x + 182 = 206

3x = 206 - 182

3x = 24

x = 24/3

x = $8

Hence, the cost of

A small bucket = x = $8

A Larger bucket = y = $13

4 0

3 years ago

Which angle is vertical to ∠3?

djverab [1.8K]

Answer:

Step-by-step explanation:

*Just a highly recommended guess.*

4 0

3 years ago

Read 2 more answers

Force is giving away tickets to a school play. She gives away 20 more adult tickets than children's tickets. She gives away 3 ti

swat32

D

hope that helps :))

8 0

3 years ago

I don’t understand this can someone help it’s a practice test please show steps.

fomenos

Using the sinusoidal function, it is found that the temperature will be below 0ºC between May and August.

<h3>What is a Sinusoidal function?</h3>

A sinusoidal function is a function that depends on a trigonometric function, having peaks according to the period and amplitude given by this function.

The function for the average monthly temperature, in m months after January, is given by:

$T(m) = 10\cos{\left(\frac{\pi}{6}\right)m} + 5$

Working with elementary angles, we have that:

$m = 10, T(0) = 10\cos{0} + 5 = 15$

$m = 3, T(3) = 10\cos{\left(\frac{\pi}{2}\right)} + 5 = 5$

$m = 6, T(3) = 10\cos{\pi} + 5 = -5$

$m = 9, T(3) = 10\cos{\left(\frac{3\pi}{2}\right)} + 5 = 5$

$m = 12, T(3) = 10\cos{2\pi} + 5 = 5$

From this, we have that it becomes negative after March, and positive before September, removing the middle two options.

Now, we have to test for April and May, that is, m = 4 and m = 5, hence:

$m = 4, T(4) = 10\cos{\left(\frac{2\pi}{3}\right)} + 5 = 0$

$m = 5, T(5) = 10\cos{\left(\frac{5\pi}{6}\right)} + 5 = -3.66$

Negative only in May, hence the temperature will be below 0ºC between May and August.

To learn more about sinusoidal function, you can take a look at brainly.com/question/18055768

7 0

2 years ago

From the quadratic equation 3x² + X - 5 = 0, find alpha square plus beta square​

From the quadratic equation 3x² + X - 5 = 0, find alpha square plus beta square