Question

Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. s squared- 5s-6=0

Answer 1

let's c..
f(s) = s^2 -5s -6
when f(s) = 0
Delta S = (-5)^2 - (4 * [-6] * 1)
= 25 + 24
= 49

therefor
Delta S > 0
which means
f(S) has two different rational solutions when f(s) = 0

Answer 2

thank you.
What about

t^2+12t+36=0

Answer 3

v^2-8v-3=0
and
w^2+3w+4=0

Answer 4

u r welcome
for ur second part
let's take f(t) , such that f(t) = t^2 +12t + 36

when f(t) = 0
delta t = 12^2 - [4 * 36 ]
= 144 - 144
= 0

when discriminant is equal to 0 the quadratic expression will have exactly one rational root
which means f(t) is a perfect square
it's actually
f(t) = (t + 6)^2

Answer 5

v^2-8v-3=0

Answer 6

w^2+3w+4=0

Answer 7

u seem to have a flow of endless questions bro,
let f(v) = v^2 -8v -3

delta v = (-8)^2 - [ 4 * (-3) ]
= 64 + 12
= 76

which means
delta v >0
which mean
f(v) has two different rational solutions when f(t) = 0

Answer 8

thank you. last one, w^2+3w+4=0

Answer 9

is it two irrational solutions?

Answer 10

let f(w) = w^2 +3w +4

delta w = (3)^2 - [ 4 * (4) ]
=9 - 16
= - 7

which means
delta w < 0
which mean
f(w) has two different irrational solutions f(w) = 0

Answer 11

thank you