Question

Please help!
For the equation x^2 + 3x + j = 0, find all the values of j such that the equation has two real number solutions.

Answer 1

what is the formula for the discriminant, which will tell you the properties of the roots?

Answer 2

wouldn't it be 4x + j = 0?

Answer 3

not quite
in the quadratic form\[ax^2+bx+c=0\] the discriminant is given by\[b^2-4ac\]what is that in your case?

Answer 4

I'm still lost

Answer 5

you have
x^2 + 3x + j = 0
the general form is
ax^2+bx+c=0
so what are the coefficients a, b, and c in your case?

Answer 6

compare\[ax^2+bx+c=0\]\[x^2+3x+j=0\]what is \(a\) in the second formula?
what is \(b\) ?
what is \(c\) ?

Answer 7

a is x, b is 3 and c is j

Answer 8

almost; b and c are right, but...
a is the coefficient of x^2
if x^2 is by itself, what is its coefficient?

Answer 9

x

Answer 10

remember that\[x^2=1x^2\]so\[a=1\]

Answer 11

so now you can use the formula for the discriminant I wrote above
what will it be in your case?

Answer 12

so it's 1x^2 + 3x + j = 0?

Answer 13

well, that's what you are given with the 1 written out explicitly (which is not really necessary)
and what is the formula for the discriminant that I wrote above?