Question

Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring?

−b b2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:

2x^2 + 7x + 3 = 0

Numerical Answers Expected!

Answer 1

hmm...

Answer 2

I think I might suicide.

Answer 3

You should expect numerical answers from yourself though

Answer 4

if
\[b^2-4ac\] is a perfect square, then your solutions are rational numbers so you can factor over the integers

Answer 5

Well that makes no sense.

Answer 6

The discriminant

Answer 7

to me

Answer 8

Do you know what discriminant is?

Answer 9

No

Answer 10

actually it makes perfect sense
the solutions to
\[ax^2+bx+c=0\] are
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 11

^ that's the quadratic formula @careless850

Answer 12

Yeah, I knew that.

Answer 13

The number of solutions depend on the discriminant.

Answer 14

I don't know what part of that formula to look at to determine when to factor though.

Answer 15

inside the radical sits the expression
\[b^2-4ac\] and if that expression is not a perfect square, like say 9 or 16, then your solutions are irrational numbers because
\[\sqrt{\text{whatever}}\] is only rational if "whatever" is a perfect square

Answer 16

If the discriminant is 0, then it has one solution.
If the discriminant is more than 0, then it has real solutions.
If the discriminant is less than 0, then it has complex solutions.

Answer 17

And a perfect square is two numbers that both sit on the axis, right?

Answer 18

^ if I correctly remember

Answer 19

so if you compute
\[b^2-4ac\] and get for example the number 5, then the two solutions are irrational and you will not be able to factor using integers

Answer 20

What are b, a and c here? @careless850

Answer 21

no a perfect square is not a number that sits on the real axis.
a perfect square is a number like
\[0,1,4,9,16,25,36,49,64,...\]

Answer 22

2 = a. 7 = b. and 3 = c.

Answer 23

Then compute \(b^2 - 4ac\)

Answer 24

7*7 = 49.

Answer 25

\( \color{Black}{\Rightarrow (7)^2 - 4(2)(3) }\)

Answer 26

Thanks.

Answer 27

49-24.

Answer 28

25.

Answer 29

And that's a perfect square :)

Answer 30

Because 5 * 5 is 25, right?

Answer 31

Yes, exactly! :D

Answer 32

or 5^2?

Answer 33

5^2 = 5 * 5

Answer 34

Alright, but what does this have to do with what my problem is asking...?

Answer 35

You got your answer.

Answer 36

1) b^2 - 4ac as sat already told you.

Answer 37

2) 25

Answer 38

Alright.