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3 years ago

What adds to get -4 and multiplies to get 16

Mathematics

1 answer:

Anna35 [415]3 years ago

3 0

Answer:

if your asking what do you have to add to negative 4 to get 16then you add 20 or if your asking what to add to get -4 I will need more info message me or comment

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

3 years ago

A 150 pound woman would recieve 24 grams of a certain medicine. How many grams should a 120 pound woman receive?

eduard

Answer:

This is matter of ratio!

42/150 = x/120. It's 33.6 grams :D

Please Mark Brainliest!!

6 0

3 years ago

In the opening scene of the movie Raiders of the Lost Ark, Indiana Jones replaces a golden statue with a bag of sand. The platfo

chubhunter [2.5K]

Answer:

1920π

Step-by-step explanation:

First, you need to find the volume of the statue in terms of pi.

Volume of cylinder formula:

V=πr²h

V=π4²15

V=π16×15

V=240π

Then, you need to find the mass of the statue.

Mass:

Mass= density × volume

Mass=20×240π

Mass=4800π

Now, you need to find the volume. Since the sand has to weigh the same as the statue, the mass is going to stay the same. To find the volume you need to do:

V=mass of sand/density

V=4800π/2.5

That gives you your answer:

1920π

Note: I had to do the exact same problem on Khan Academy. This is right.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7B3%7D%7B16%7D%20%7D%20" id="TexFormula1" title=" \sqrt{ \frac{3}{16}

sweet-ann [11.9K]

Hello!
When you have a non-exact root (irrational number)

$\sqrt{ \frac{3}{16} } \to \frac{ \sqrt{3} }{ \sqrt{16} } \to \boxed{\boxed{\frac{ \sqrt{3} }{4} }}\Longleftarrow(irrational\:number)\end{array}}\qquad\quad\checkmark$

7 0

4 years ago

What equals to 20 and 84

Charra [1.4K]

Two is equivalent to twenty and 84

4 0

3 years ago

Read 2 more answers

What adds to get -4 and multiplies to￼ get 16

What adds to get -4 and multiplies to get 16