(Please help, due by midnight PST in 2hours) Find x and y.

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:

2

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

Three boxes are shipped on a truck,. Each box has a base of 16 square feet. Two of the boxes have a height of 3 feet and one box

vodka [1.7K]

I believe the answer is 176 cubic feet

7 0

3 years ago

Read 2 more answers

2<br>Decrease R420 in the ratio 4:7

Oxana [17]

Step-by-step explanation:

Let the numbers are 4x and 7x. According to the question if each number is increased by 20, the ratio becomes 7 : 9.

Then,

( 4x + 20 ) : ( 7x + 20 ) = 7 : 9

9( 4x + 20 ) = 7( 7x + 20 )

9( 4x ) + 9( 20 ) = 7( 7x ) + 7( 20 )

9( 20 ) - 7( 20 ) = 7( 7x ) - 9( 4x )

2( 20 ) = 49x - 36x

40 = 13 x

40 / 13 = x

Therefore, number are :–

4 x = 4( 40 / 13 ) = 160 / 13

7 x = 7( 40 / 13 ) = 280 / 13

4 0

3 years ago

Given:• PQRS is a rectangle.• mZ1 = 50°Р21SRWhat is mZ2?130°85°70°65°

Over [174]

To answer this question, we need to recall that: "the diagonals of a rectangle bisect each other"

Thus, if we assign the point of intersection of the two diagonals in the rectangle as point O, we can say that the triangle OQR is an "isosceles triangle". Note that this is because the lengths OR and OQ are equal since we know that: "the diagonals of a rectangle bisect each other". See the below diagram for clarity.

Now, we have to recall that:

- the base angles of any isosceles triangle are equal. This is a fact, and this means that the angles

- also the sum of all the angles in any triangle is 180 degrees

Now, considering the isosceles triangle OQR, we have that:

$\angle OQR+\angle ORQ+\angle ROQ=180^o$

Now, since the figure already shows that angle $m\angle2+\angle ORQ+50^o=180^o$ Now, since we have established that the base angles $m\angle2+m\angle2+50^o=180^o$ we can now solve the above equation for m<2 as follows:

$\begin{gathered} m\angle2+m\angle2+50^o=180^o \\ \Rightarrow2m\angle2+50^o=180^o \\ \Rightarrow2m\angle2=180^o-50^o \\ \Rightarrow2m\angle2=130^o \\ \Rightarrow m\angle2=\frac{130^o}{2}=65^o \end{gathered}$

Therefore, the correct answer is: option D

7 0

1 year ago

Paula has 6 video games. Myles has 1 more video game than paula. Which could you use to find how many video games in all.

IrinaVladis [17]

Paula = 6 video games

Myles = 1 video game + Paula(6 video games)

P + M = Total video games

M = 1 + P

P = 6

P + M = 6 + 1 = 7

4 0

4 years ago