Question

given exact and approximate solutions to three decimal places
x^2-5x+3=0?

Answer 1

this is a job for... superman! as long as superman knows how to use the quadratic equation.

Answer 2

are you familiar with the quadratic equation?

Answer 3

a little not a lot though

Answer 4

what do you know about it?

Answer 5

that its kina of like reg equation that you wht you do on one side you do the other side right

Answer 6

well the "quadratic formula" tells us how to find the roots of a quadratic equation. the "roots" are the places that it is equal to 0. have you seen it before?

It says that if an equation is of the form
\[ax^2 + bx + c\]
Then the roots can be found at
\[{-b \pm \sqrt{b^2 - 4ac}}\over2a\]

Answer 7

yes

Answer 8

so what are a, b, and c in the equation you gave originally?

Answer 9

a would be x^2 b 5x c would be 3 right

Answer 10

very close - a, b, and c are just the coefficients (the number) in front of the x^2 and x terms

Answer 11

huh?

Answer 12

Remember that "x^2" is like saying 1 * x^2. Given that, what are the values of a, and b?

Answer 13

x2 and 5x

Answer 14

Well remember, a b and c are the coefficients, not the part with the 'x'. a=1, b=-5, c=3. Given that, can you plug those into the quadratic formula now?

Answer 15

so my equation would look like this right?
1x^2+5x+3

Answer 16

remember b=-5, so it is -5x, not +5x. But can you plug those numbers we got for a, b, and c into the quadratic formula - the one that starts with -b / 2a, that I put above?

Answer 17

im so lost

Answer 18

OK. Do you see hte quadratic formula I gave?

Answer 19

yes

Answer 20

which one are you looking at?

Answer 21

the ax^2+bx+c

Answer 22

do you see the other formula I gave, below it? the one that tells you the roots?

Answer 23

yea

Answer 24

ok can you plug the values of A, B, and C into that?

Answer 25

hold on

Answer 26

alright it would be -5sqrt 5^2-4(1)(3) /2*1

Answer 27

right?

Answer 28

well remember b is -5, not +5

Answer 29

then what is the correct answer

Answer 30

if b is -5, then what is -b?

Answer 31

5

Answer 32

right. and the formula starts with -b so it should start with 5, but you wrote -5.

Answer 33

so my answer for the whole problem would be 5+-sqrt13/3

Answer 34

(5 +- sqrt(13)) / 2

Answer 35

thats what i had right,that is the right answer is it

Answer 36

im sorry i had over 3 instead of 2

Answer 37

you divided by 3

Answer 38

the denominator is 2a, and a=1

Answer 39

i know i was adding 2+1 instead of 2*1

Answer 40

that's not right, the denominator is 2a, which is 2*a

Answer 41

so answer is then 5sqrt13/2 right

Answer 42

so then what would be the solutions

Answer 43

don't forget the plus and minus. there are two answers, one with plus and one with minus. Where the original equation said \[\pm\], that means you have two answers, once where it's plus and once where it's minus. So the two answers are

\[{5 + \sqrt{13} }\over2\]
and
\[{5 - \sqrt{13} }\over2\]

Answer 44

what about the approximate solution which i dont understand what that is

Answer 45

well what we just wrote are the two exact solutions. To find the approximate solutions to 3 decimal places you then compute the square root of 13 with your calculator and do the final steps to come up with a single number (one number for each of the two solutions)

Answer 46

3.6055 is what i got. so the answer then would be 3.61 rght

Answer 47

that's the square root of 13, yes. now you substitute that number in to get the two solutions.

Answer 48

the first one would be 4.302
and the second one would be 0.697 am i right

Answer 49

yayyyyy! yes that's the final answer