Question

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?
a) m>12/49
b) m<12/49
c) m<49/12
d) m> 49/12

Answer 1

Do you have any pictures for this question?

Answer 2

Okay, perfect :)

Answer 3

Hold on, I'm working it out on paper.

Answer 4

alright c:

Answer 5

Alrighty. The quadratic formula (a part we call the "discriminant") is defined by the variables that are inside the square root, and is denotated by the delta

Answer 6

Δ=b2−4ac

Answer 7

Whenever we solve a quadratic equation that is complete and we analyze the discriminant,

Answer 8

we get 3 scenarios:
if→Δ>0=>∃x1,x2/ax2+bx+c=0

Answer 9

This just means: "if the discriminant is greater than zero, there will exist two x-intercepts"
And for the second scenario:
if→Δ=0→∃xo/ax2+bx+c=0

Answer 10

This means that if the discriminant is equal to zero, there will be one and only one x-intercept
And for the last scenario: (if→Δ<0→∃x∉R/ax2+bx+c=0)

This means that if our discriminant is less than zero, there will be no x-intercepts
So, if we take your excercise and analyze the the discriminant
(which is 3x2+7x+m=y)
we can find the values that satisfy y=0
3x2+7x+m=0
than we can analyze the discriminant:
Δ=72−4(3)(m)
we are only interested in the values that make the discriminant equal zero
72−4(3)(m)=0
so all you have to do is solve for "m"

Answer 11

im very confused

Answer 12

Oh no :(
I'll simplify this

to find the intercepts of the graph, you have to solve for "m"

Answer 13

D is your answer