Question

18. Use the discriminant to find the number of real solutions of the equation 3x2 – 5x + 4 = 0. Show your work.

Answer 1

do u know the discriminant formula?

Answer 2

no

Answer 3

it islike a/ something then b / something

Answer 4

its D=\[\sqrt{b ^{2}-4ac}\]

Answer 5

HI!!

Answer 6

u know what is a ,b,c right?

Answer 7

actually the "discriminant" is just \[b^2-4ac\]

Answer 8

oh yeah no root sorry!

Answer 9

would a be 3 b 5 and c 4?

Answer 10

almost correct!

Answer 11

b is -5

Answer 12

okay.. after i have all that what do i do?

Answer 13

u just plug these values in the above expression that is \[b^2 - 4ac\]

Answer 14

what do u get?

Answer 15

okay so i would go -5^2 -3 ?

Answer 16

8?

Answer 17

no.. where is the "4*a*c" part?

Answer 18

i don't know how to do this ?

Answer 19

48

Answer 20

\[b ^{2}-4ac = (-5)^2 - (4*3*4)\]

Answer 21

yeah! 4ac is 48..what is D (as a whole)

Answer 22

i don't know

Answer 23

D=b^2−4ac..so just evaluate the above exp i have written..

Answer 24

(-5)^2-48

Answer 25

-58?

Answer 26

no.. (-5)^2=25
so 25-48=-23 ok?

Answer 27

@jamie2012 ?

Answer 28

so here D = -23

Answer 29

yes. it's -23? how did you get that?

Answer 30

and..remember this:
if D>0 -->2real roots
D=0 -->2 equal real roots-->so one real root
D<0 -->No real roots
So what will be the answer here?

Answer 31

what is \[b ^{2}\] ?

Answer 32

it would be 2 real roots ?

Answer 33

first we will clear ur doubt about -23 ok?

Answer 34

okay

Answer 35

so what is b here?

Answer 36

-5

Answer 37

ya..now square it

Answer 38

?

Answer 39

can't don't know how to

Answer 40

squaring is multiplying the same number twice..Ex: (-2)^2 = 4

Answer 41

ok?

Answer 42

okay

Answer 43

so what is (-5)^2 ?

Answer 44

its nothing but -5 * -5

Answer 45

=?

Answer 46

-10

Answer 47

this is multiplication..not addition

Answer 48

25?

Answer 49

yeah correct!!

Answer 50

so u have found b^2.. and u already told me 4ac is 48..so subtract both..

Answer 51

25-48

Answer 52

23

Answer 53

no..always put the "bigger" number's sign..so its -23..

Answer 54

now D=-23..so is D>0 or D<0?

Answer 55

i did

Answer 56

d>0

Answer 57

no it would be < cuz its -23?

Answer 58

no..D>0 means D is positive..is -23 positive?

Answer 59

no it would be < cuz its -23?

Answer 60

ya! so what is the answer?

Answer 61

d=<- 23?

Answer 62

why = ?

Answer 63

D<0 thats it

Answer 64

idk..

Answer 65

and..remember this:
if D>0 -->2real roots
D=0 -->2 equal real roots-->so one real root
D<0 -->No real roots
So what will be the answer here?

Answer 66

what does D<0 mean ?

Answer 67

check from the above facts..

Answer 68

no root

Answer 69

u mean no "real" root right? (coz the word real is very important..u will learn why in higher classes )

Answer 70

yes i do

Answer 71

Good!! Thats correct!

Answer 72

WELL DONE!

Answer 73

oh thank you so much

Answer 74

u r welcome!

Answer 75

can you help with another one?