Melody

just wondering if anyone could please shed some light on this one for me?. If we consider the equation: ax^2+bx+a=0, then:

Prove that IF this equation has only one rational root, then b=+-2a.

OR if you allowed to take short cuts you could say that the quadratic formula gives the roots as

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \)

but in your quadratic c=a  so

\(x = {-b \pm \sqrt{b^2-4a^2} \over 2a}\)

This will have exactly one solution when

\(b^2-4a^2=0\)

Continue the same as for my first 'proper' solution.

Hi,     

ax^2+bx+a=0

\(ax^2+bx+a=0\\ ax^2+bx=-a\\ x^2+\frac{b}{a}x = -1\\ x^2+\frac{b}{a}x + (\frac{b}{2a} )^2 = -1 + (\frac{b}{2a} )^2 \\ (x+ \frac{b}{2a} )^2 = -1 + (\frac{b}{2a} )^2 \\ (x+ \frac{b}{2a} )^2 = -\frac{4aa}{4aa} + \frac{bb}{4aa} \\ (x+ \frac{b}{2a} )^2 = \frac{bb-4aa}{4aa} \\ \)

\((x+ \frac{b}{2a} )^2 = \frac{bb-4aa}{4aa} \\ x+ \frac{b}{2a} = \pm \sqrt{ \frac{bb-4aa}{4aa} } \\ x = - \frac{b}{2a} \pm \sqrt{ \frac{bb-4aa}{4aa} } \\ x = - \frac{b}{2a} \pm \frac{1}{2a} \sqrt{ bb-4aa } \\ a\ne0\\ \mbox{There will be only one root when }\\ b^2-4a^2=0 \\ (b-2a)(b+2a)=0\\ b=\pm2a \)

\(tan\theta=(6-1.75)/18\\ \)

(180/pi)*atan((6-1.75)/18) = 13.2848664848799147 degrees

Hi Juriemagic,

Yes earlier your name was displayed as being logged on.   ://    That is an enigma.     

I hope this problems is fixed soon. ://

how long does it take for budoy's car to change its velocity from 12 m/s to 25 m/s if the acceleration id 5 m/s?

I am sure that you mean  a=5m/s^2

u=12  v =25  a=5  t=?

v=u+at

25=12+5t

13=5t

t=13/5 = 2.6 seconds

Thank you for all the flattery Juriemagic :))    

You need to get used to using Desmos Graphing calculator (or any graphing calc) to help you understand what is happening with these problems.

Learning to anticipate what a wide variety of graphs will look like will help you with many problems. 

I see that you are logged on at present.  I hoope this means that you log on problems are over  

Tues 10/11/15

1)  Trig equation

      http://web2.0calc.com/questions/trig_67661#r1

2)  Modular arithmetic     Thanks Alan

     http://web2.0calc.com/questions/43-p-mod-247-17#r4

3)  Venn diagram with probabilities.    Thanks CPhill

     http://web2.0calc.com/questions/venn-diagram_1#r1

4) Speed distance and direction    Thanks CPhill

    http://web2.0calc.com/questions/two-jets-leave-denver-at-9-00-a-m-one-flying-east-at-a-speed-50kn-h-greater-than-the-other-which-is-traveling-west-at-11-00-a-m-the-planes-are-2500-km#r1

5)  Manipulating log equations     Thanks Heureka

   http://web2.0calc.com/questions/two-jets-leave-denver-at-9-00-a-m-one-flying-east-at-a-speed-50kn-h-greater-than-the-other-which-is-traveling-west-at-11-00-a-m-the-planes-are-2500-km#r1

6)  Devivative of a^x       Thanks Chris  

    http://web2.0calc.com/questions/derivative-of-a-x-proof#r2

@@ What is Happening?  [Wrap4]    Mon 9/11/15   Sydney, Australia Time 7:46pm   ♪ ♫

Hi all,

Our great answers today were contributed by Alan, Lamblamb, Maximillian, CPhii and Heureka.  Thank you. 

Repeat request:

There is a post below where I have invited people to discuss their views of the forum.  All sensible thoughts will be greatly appreciated.

f^3(x)+f(x)=lnx,x>0

prove that f is constant at x=1

I actually do not understand the questions.  What do you mean, f is a constant at x=1 ??

(My play)

f^3(1)+f(1)=ln1

f^3(1)+f(1)=0

f(1) [f^2(x)+1]

f(1)=0    or    f^2(x)=-1

In the real number system the only solution is f(1)=0

Where is the pie button!!

top left, next to [2nd]