Question

Algebra 2 help. Medal!

Answer 1

??

Answer 2

@ganeshie8

Answer 3

heard of `discriminant` before ?

Answer 4

I don't know exactly what it is but I know the formula -b-4ac

Answer 5

\(\large b^2 - 4ac\) is called the discriminant

Answer 6

start by finding the discriminant of first function :
\(\large f(x) = x^2+6x-16\)

Answer 7

ok so 6^2-4(1)(-16)

Answer 8

\(\large a = 1\)
\(\large b = 6\)
\(\large c = -16\)

discriminant =\(\large b^2-4ac = ?\)

Answer 9

Yes ! simplify

Answer 10

is it plus or minus 64

Answer 11

its either -28 or 100 but I don't know which one

Answer 12

im pretty sure its 100

Answer 13

6^2-4(1)(-16)

36 + 64

100

Answer 14

You're right !

Answer 15

sweet now how do I figure out if its 2 irrational solutions or 2 rational solutions

Answer 16

and since the dicriminant is a perfect square(100 = 10^2), f(x) must have `Two real rationals solutions`

Answer 17

ohhhhh ok thank you! so what about the second equation

Answer 18

find the discriminant for second equation also

Answer 19

it would be 6^2-4(1)(1) so the next one would be 32

Answer 20

Yes !

Answer 21

but im still confused with the conditions...

Answer 22

and since the dicriminant is > 0, but not a perfect square), g(x) must have `Two real irrational solutions`

Answer 23

ohhhh yes I get it now!!! :) :) :)

Answer 24

Here are the conditions :

discriminant > 0, and a perfect square : two different real RATIONAL solutions
discriminant > 0, and NOT a perfect square : two different real IRRATIONAL solutions


discriminant = 0 : two same real rational solutions
discriminant < 0 : two complex solutions

Answer 25

good :)

Answer 26

ok thank you! can you help with a couple more?

Answer 27

I'll try... ask them in a separate post :)

Answer 28

ok hang on