I need help with these problems please..

katy · 2005-12-29 06:24:25

I am doing some math problems and these are the ones I can not solve..:

1)The sum of 2 numbers is 34.Find the numbers if the sum of their squares is a minimum.
2)Without solving the equation find the discriminant and state the nature of the roots: 2x^2+3x-10
(in question #2 how can you find the discriminant and state the nature of the roots just by looking???)

Many thanks to the people who can help me with this......

Katy

krassi_holmz · 2005-12-29 06:53:59

x+y=34 =>
y=34-x
Substitute in 1:
Let {is} means "must be"
x^2+(34-x)^2 {is} min =>
x^2+34^2-68x+x^2 {is} min =>
2x^2-68x {is} min =>
2(x^2 - 34x) {is} min =>
x^2 - 34x {is} min =>
x^2 - 2.17.x {is} min =>
(here is the thin moment...)
x^2-2.17x+17^2 {is} min =>
(x-17)^2 {is} min =>
(x-17)^2=0
x=17
y=34-17=17

krassi_holmz · 2005-12-29 06:59:08

Plot:

Last edited by krassi_holmz (2005-12-29 07:01:14)

krassi_holmz · 2005-12-29 07:04:33

I'm just guessing...
X1/2= (+-sqr(89)-3)/4?

Last edited by krassi_holmz (2005-12-29 07:07:33)

krassi_holmz · 2005-12-29 07:09:26

That was joke

Actually I don't know how to solve it without solving it.

mathsyperson · 2005-12-29 07:12:26

For 2) it doesn't ask you to find the values of x, just the discriminant.
The discriminant is the bit inside the square root of the quadratic equation:

In this case, the discriminant would be 3² - 4*2*(-10) = 89.
Because it is positive, this shows that both roots will be real and distinct.

krassi_holmz · 2005-12-29 07:30:22

Of course, but I thought that you are not permissed to calculate the discriminant.

And something else :
10>3^2 => discriminant is > 0.

katy · 2005-12-29 07:44:09

thanks a lot guys....
I have one more question:
1)Explain when a parabola will have 2 real roots, 2 imaginary roots, and 2 equal real roots.Explain what characteristics the discriminant will have for the above cases
My answer is:
discriminant>0 (2 real roots)
discriminant<0(2 imaginary roots)
discriminant=0(2 equal real roots)
is it right?

krassi_holmz · 2005-12-29 07:57:03

For the 1b problem.
The parabloa is quadratic surve. So you're right.

mikau · 2005-12-29 08:35:32

2 real roots when the discriminant is positve. 2 imaginary roots when the discriminant is negative. Two equal roots when the discriminant is zero.

If you forget what the descriminant is:

You can find the roots of a quadratic equation of the form:

ax^2 + bx + c

using the quadratic formula:

(-b +- √ b^2 - 4ac)/2a

the part of the formula inside the radical side is the descriminant.

√ b^2 - 4ac

when the descriminant (b^2 - 4ac) is positive, it has two real roots. When it is negative, it will require the square root of a negative number and thus only has imaginary roots. When the discriminant is 0 the roots will be -b/2a + 0, and -b/2a - 0 which are obviously equal.

katy · 2005-12-29 10:21:51

thanks a lot guys...i get them now...you all are smart.
katy.

mikau · 2005-12-29 11:04:28

Nah we just pretend to be.

katy · 2005-12-29 11:10:01

mikau wrote:

Nah we just pretend to be.

lol...of course you all are....I am the stupid one..hehehe

mikau · 2005-12-29 11:20:02

Not stupid. You just need practice. Math isn't hard. It just takes some getting used to.

krassi_holmz · 2005-12-29 11:24:47

I presentiment katy will become bery good in Maths.

mikau · 2005-12-29 12:35:55

bery good? are you being funny?

Math Is Fun Forum

#1 2005-12-29 06:24:25

I need help with these problems please..

#2 2005-12-29 06:53:59

Re: I need help with these problems please..

#3 2005-12-29 06:59:08

Re: I need help with these problems please..

#4 2005-12-29 07:04:33

Re: I need help with these problems please..

#5 2005-12-29 07:09:26

Re: I need help with these problems please..

#6 2005-12-29 07:12:26

Re: I need help with these problems please..

#7 2005-12-29 07:30:22

Re: I need help with these problems please..

#8 2005-12-29 07:44:09

Re: I need help with these problems please..

#9 2005-12-29 07:57:03

Re: I need help with these problems please..

#10 2005-12-29 08:35:32

Re: I need help with these problems please..

#11 2005-12-29 10:21:51

Re: I need help with these problems please..

#12 2005-12-29 11:04:28

Re: I need help with these problems please..

#13 2005-12-29 11:10:01

Re: I need help with these problems please..

#14 2005-12-29 11:20:02

Re: I need help with these problems please..

#15 2005-12-29 11:24:47

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#16 2005-12-29 12:35:55

Re: I need help with these problems please..

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