X^2+x+3 factor the polynomial

Mathematics

1 answer:

Zarrin [17]4 years ago

7 0

Answer:

x = -1/2 + (i/2)√11 and x = -1/2 - (i/2)√11

Step-by-step explanation:

This polynomial is a quadratic. Its coefficients are a = 1, b = 1 and c = 3.

Thus, the discriminant b^2-4ac is 1^2 - 4(1)(3), or 1 - 12, or -11.

Because the discriminant is negative, the roots are complex.

The roots are:

-1 ±√(-11) -1 ±i√11

x = --------------- = ----------------, so x = -1/2 + (i/2)√11 and x = -1/2 - (i/2)√11

2 2

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The diameter of each wheel of a bicycle is 27 inches. If you are traveling at a speed of 20 miles per hour on this bicycle, thro

klasskru [66]

Notice, you've got a diameter in inches
and a linear velocity in miles
thus, you'd need to convert first

$\bf v=rw\implies \cfrac{v}{r}=w\qquad 
\begin{cases}
v=\textit{linear speed}\\
r=radius\\
w=\textit{angular speed}\\
 --------------\\
v=20\frac{mi}{h}\\
r=\frac{diameter}{2}=\frac{27}{2}
\end{cases}
\\\\
\textit{now, converting 20miles to inches}
\\\\
\cfrac{20mi}{h}\cdot \cfrac{5280ft}{mi}\cdot \cfrac{12in}{ft}\implies \cfrac{20\cdot 5280\cdot 12\ in}{h}\impliedby v
\\\\\\
\cfrac{1267200\frac{in}{h}}{\frac{27}{2}in}=w$

now, whatever that is, you'll need to divide it by a revolution, recall, a revolution is $2\pi$
thus $\bf \cfrac{\qquad \boxed{\cfrac{1267200\frac{in}{h}}{\frac{27}{2}in}}\qquad }{2\pi }=revolutions$

7 0

3 years ago

Read 2 more answers

Pls send the answer

luda_lava [24]

Answer:

$a = \dfrac{46}{17}$

$b = 0$

Step-by-step explanation:

$\dfrac{2\sqrt{5} + \sqrt{3}}{2\sqrt{5} - \sqrt{3}} + \dfrac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} + \sqrt{3}} =$

$= \dfrac{2\sqrt{5} + \sqrt{3}}{2\sqrt{5} - \sqrt{3}} \times \dfrac{2\sqrt{5} + \sqrt{3}}{2\sqrt{5} + \sqrt{3}} + \dfrac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} + \sqrt{3}} \times \dfrac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} - \sqrt{3}}$