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2 years ago

Pierre stands on a level ground at the point P, 5 metres from O.

Mathematics

1 answer:

Zolol [24]2 years ago

5 0

I think there is data that is missing. Please attach the drawing so that to help you

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P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

2 years ago

Subtract and simplify. (2y + 14.6m + 3.8) – (34.8m + 15.6 + 2y)

irina1246 [14]

Answer:

-20,2m-11,8

Step-by-step explanation:

rewrite it

2y+14,6m+3,8-(34,8m+15,6-2y)

remove the opposites

and then simplify

-20,2m-11,8

im not sure if this makes sense

5 0

2 years ago

Read 2 more answers

Its not very clear but if someone could help me with the answers that would be great

Pie

Can’t see it properly...

6 0

2 years ago

How do you write 0.000056 in scientific notation?

anygoal [31]

5.6 × 10^-5 = 0.000056

8 0

3 years ago

If (8^2)p = 8^4, what is the value of p? 2 3 4 6

Assoli18 [71]

Answer:

Step-by-step explanation:

8²p=8^4

64p=4096

p=64

p could also equal 2

8^2x2=8^4

3 0

1 year ago