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3 years ago

Tìm nghiệm của đa thức 2x² + 5x

Mathematics

2 answers:

Neko [114]3 years ago

8 0

Answer:

$2x^2+5x$

$=2xx+5x$

$=x\left(2x+5\right)$

Hope it helps u

madreJ [45]3 years ago

4 0

Answer:

this is this because of PTI

Step-by-step explanation:

pto explain it to me on Monday and Friday Saturday morning

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3 years ago

Simplify the square root of 3 times the fifth root of 3.

bogdanovich [222]

Answer:

<h2><em>Three to the three fifths power.</em></h2>

Step-by-step explanation:

The given expression is

$\sqrt{3\sqrt[5]{3} }$

To simplify this expression, we have to use a specific power property which allow us to transform a root into a power with a fractional exponent, the property states:

$\sqrt[n]{x^{m}}=x^{\frac{m}{n}}$

Applying the property, we have:

$\sqrt{3\sqrt[5]{3}}=\sqrt{3(3)^{\frac{1}{5}}}=(3(3)^{\frac{1}{5}})^{\frac{1}{2}}$

Now, we multiply exponents:

$(3(3)^{\frac{1}{5}})^{\frac{1}{2}}\\3^{\frac{1}{2}}3^{\frac{1}{10}}$

Then, we sum exponents to get the simplest form:

$3^{\frac{1}{2}}3^{\frac{1}{10}}=3^{\frac{1}{2}+\frac{1}{10}} =3^{\frac{10+2}{20}}=3^{\frac{12}{20}} \\\therefore \sqrt{3\sqrt[5]{3}}=3^{\frac{3}{5} }$

Therefore, the right answer is <em>three to the three fifths power.</em>

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4 years ago

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3 years ago

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Question no 6 answer

ExtremeBDS [4]

Answer:

a = 1
b = -28
P(x) = (x +2)(x -3)(x^2 +3x +10)

Step-by-step explanation:

a) Since x+2 is a factor, we know P(-2) = 0.

P(x) = (((x +2)x +a)x +b)x -60

Then the value of P(-2) is ...

P(-2) = 0 = (((0)(-2) +a)(-2) +b)(-2) -60 = (-2a +b)(-2) -60 = 4a -2b -60

We know the remainder from division by (x+3) is 60, so

P(-3) = 60 = (((-3+2)(-3) +a)(-3) +b)(-3) -60 = ((3+a)(-3) +b)(-3) -60

= (-9 -3a +b)(-3) -60 = 27 +9a -3b -60

93 = 9a -3b

These two equations can be put into standard form:

2a -b = 30

3a -b = 31

Then we have the solution ...

a = 1 . . . . . (by subtracting the first equation from the second)

-28 = b . . . by substituting into the first equation

b) To show that (x-3) is a factor we need to evaluate P(3).

P(3) = (((3 +2)(3) +1)(3) -28)(3) -60 = (48 -28)(3) -60 = 0

The function value is 0, so (x -3) is a factor.

c) We want to find Q(x) = x^2 +cx +d such that ...

(x +2)(x -3)Q(x) = P(x)

(x^2 -x -6)(x^2 +cx +d) = x^4 +2x^3 +x^2 -28x -60

x^4 +(c-1)x^3 +(-6-c+d)x^2 +(-6c-d)x -6d = x^4 +2x^3 +x^2 -28x -60

This gives rise to the equations ...

c -1 = 2 ⇒ c = 3

-6d = -60 ⇒ d = 10

Then P(x) can be factored as ...

P(x) = (x +2)(x -3)(x^2 +3x +10)

_____

<em>Comment on the attached graph</em>

I like to use a graphing calculator to find real roots of higher-degree polynomials. This graph shows the real zeros to be -2 and +3, so we know that (x +2) and (x -3) are factors. The green curve is P(x) with those factors divided out, so is a graph of Q(x). The vertex of that graph tells us that ...

Q(x) = (x +1.5)^2 +7.75 = x^2 +3x +10

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3 years ago