Question

Medal and Fan!
A quadratic equation is shown below:

3x2 - 16x + 2 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (3 points)

Part B: Solve 9x2 + 3x - 2 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (4 points)

Part C: Solve 3x2 - 10x + 2 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Answer 1

@jim_thompson5910 could you help me please?

Answer 2

@texaschic101

Answer 3

@misty1212

Answer 4

\[3x^2 - 16x + 2 = 0\] i assume by "radicand" they really mean "discriminant"

Answer 5

\[b^2-4ac\] or in your case
\[(-16)^2-4\times 3\times 2\]

Answer 6

Okay so -232

Answer 7

i get \(232\) a positive number
that means there are "two real solutions"

Answer 8

Right sorry I didnt take in account the negative times a negative

Answer 9

So part a = 232 plus all the work shown and two real solutions :)

Answer 10

9x^2+3x-2=0

Answer 11

What is my first step to doing part b? :)

Answer 12

me scrolling up to read the question!!

Answer 13

\[9x^2 + 3x - 2 = 0 \] right?

Answer 14

yes :D

Answer 15

by some miracle this factors as
\[(3x-1)(3x+2)=0\]

Answer 16

set each factor equal to zero and solve, i.e. solve
\[3x-1=0\] and then solve
\[3x+2=0\]

Answer 17

okies so
3x-1=0
add 1 to both sides
3x=1
divide 3
x=.33 repeating

Answer 18

3x+2=0
subtract 2 by each side
3x=-2
divide by 3
x= .66

Answer 19

lol put away your calculator dear

Answer 20

2/3 we leave it in fraction form?

Answer 21

okay
x= 1/3
and
x=-2/3

Answer 22

right :3?

Answer 23

yes

Answer 24

Okay great! Part C: Solve 3x2 - 10x + 2 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Answer 25

What equation do we use this time :D

Answer 26

use the quadratic formula
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] with '
\[a=3,b=-10,c=2\]

Answer 27

\[x=10+\sqrt{100-(-4)(3)(2)} \]

Answer 28

which is all over 2(3) @satellite73 ?

Answer 29

lets start in the square root, 100-(-4)(3)(2) = 100+24=124

Answer 30

10+SQRT of 124 / 6= x

Answer 31

that is a good start

Answer 32

but the square root of 124 isnt a whole number

Answer 33

true

Answer 34

we got a mistake here i didn't catch

Answer 35

\[\sqrt{b^2-4ac}=\sqrt{(-10)^2-4\times 3\times 2}=\sqrt{100-24}\]

Answer 36

Oops! that makes it easier!

Answer 37

so
\[\frac{10\pm\sqrt{76}}{6}\]

Answer 38

that is still not a whole number... @satellite73

Answer 39

what do I do now is that the final answer?

Answer 40

@satellite73 ?

Answer 41

you can write it in simplest radical form if you like

Answer 42

Thank you so much for all your help <3 :)

Answer 43

\[\sqrt{76}=\sqrt{4\times 19}=2\sqrt{19}\]

Answer 44

so\[\frac{10\pm2\sqrt{19}}{6}=\frac{5\pm\sqrt{19}}{3}\]

Answer 45

yw

Answer 46

be careful when you cancel, you have to cancel from both terms

Answer 47

and yes it is not a whole number, which is why you can't factor using integers