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3 years ago

Hi, could someone solve this parametric system?

Mathematics

1 answer:

baherus [9]3 years ago

4 0

9514 1404 393

Answer:

(x, y, z) = ((7 -2k)/(-31 +7k), (-29 +7k)/(-31 +7k), 1/(31 -7k))

Step-by-step explanation:

The system can be solved by any of your favorite methods. Treat k as you would any number.

My row reduction software says the solution is ...

(x, y, z) = ((7 -2k)/(-31 +7k), (-29 +7k)/(-31 +7k), 1/(31 -7k))

Clearly, k ≠ 31/7.

The augmented coefficient matrix is attached.

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Find all the zeros of the polynomial function P(x) x^4-4x^3 -5x^2+38x- 30

worty [1.4K]

Answer:

The zeros of the polynomial function are 1, -3, 3+i and 3-i.

Step-by-step explanation:

The given function is

$P(x)=x^4-4x^3-5x^2+38x-30$

We can find a zero of the given function by hit and trial method.

Substitute x=1 in the given function.

$P(1)=(1)^4-4(1)^3-5(1)^2+38(1)-30$

$P(1)=0$

The value of function is 0 at x=1 it means (x-1) is a factor of given function.

Substitute x=-3 in the given function.

$P(-3)=(-3)^4-4(-3)^3-5(-3)^2+38(-3)-30$

$P(-3)=0$

The value of function is 0 at x=-3 it means (x+3) is a factor of given function.

$(x-1)(x+3)=x^2 + 2 x - 3$

Divide the given function by $x^2 + 2 x - 3$ , to get remaining factors.

$\frac{x^4-4x^3-5x^2+38x-30}{x^2 + 2 x - 3}=x^2 - 6 x + 10$

So, the factor form of given function is

$P(x)=(x - 1) (x + 3) (x^2 - 6 x + 10)$

Quadratic formula: If a quadratic equation is $ax^2+bx+c=0$ , then

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

Using quadratic formula find the zeroes of $x^2 - 6 x + 10$ .

$x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(10)}}{2(1)}$

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

$x=\frac{6\pm 2i}{2}$ $[\because \sqrt{-1}=i]$

$x=3\pm i$

Therefore the zeros of the polynomial function are 1, -3, 3+i and 3-i.

3 0

3 years ago

Plz help me owo thanks

IrinaK [193]

Answer: D

Step-by-step explanation:

XD uwu lol

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3 years ago

Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measur

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Answer:

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Step-by-step explanation:

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3 years ago

You received $112 in all selling paintings. You sold one painting for $27

Contact [7]

Answer:

Step-by-step explanation:

17x = 85

17x/17 = 85/17

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3 years ago

I appreciate the help and if you don’t mind can someone please help me with this one too

Allisa [31]

Answer:

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Step-by-step explanation:

soln:

given,

$8=1 hour

or,$1=1/8 hour

so,

$64=64*1/8 hour

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3 years ago