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**katy****Member**- Registered: 2005-12-28
- Posts: 14

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

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Plot:

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I'm just guessing...

X1/2= (+-sqr(89)-3)/4?

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

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

That was joke

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

IPBLE: Increasing Performance By Lowering Expectations.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

Why did the vector cross the road?

It wanted to be normal.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

And something else :

10>3^2 => discriminant is > 0.

IPBLE: Increasing Performance By Lowering Expectations.

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**katy****Member**- Registered: 2005-12-28
- Posts: 14

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?

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

For the 1b problem.

The parabloa is quadratic surve. So you're right.

IPBLE: Increasing Performance By Lowering Expectations.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

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.

A logarithm is just a misspelled algorithm.

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**katy****Member**- Registered: 2005-12-28
- Posts: 14

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

katy.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Nah we just pretend to be.

A logarithm is just a misspelled algorithm.

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**katy****Member**- Registered: 2005-12-28
- Posts: 14

mikau wrote:

Nah we just pretend to be.

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

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

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

A logarithm is just a misspelled algorithm.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I presentiment katy will become bery good in Maths.

IPBLE: Increasing Performance By Lowering Expectations.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

bery good? are you being funny?

A logarithm is just a misspelled algorithm.

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