Question

What adds to -10 and multiplies to 6?

Answer 1

?? Confusing. ANymore info?

Answer 2

No this is a step to factoring :(

Answer 3

What answer did you get?

Answer 4

or did you try it yet

Answer 5

The equation is 3x2 - 10x + 2 = 0, so I add the last term and first coefficient and then find factors of that number that adds to the middle term

Answer 6

..... What?!?!

Answer 7

Yeah

Answer 8

...

Answer 9

So basically factors of 6 that add to -10

Answer 10

(or subtract I guess)

Answer 11

I outsourced because this is a tad ridiculous and I don't want to write out every possible combination of numbers that add (or add negatives) to get -10 because it's literally infinite

Answer 12

3x^2 -10x + 2 = 0 is in the form ax^2 + bx + c = 0

where
a = 3
b = -10
c = 2

plug these values into the discriminant formula

d = b^2 - 4ac
d = (-10)^2 - 4(3)(2)
d = 100 - 24
d = 76

the discriminant is positive but it's not a perfect square. So we can't factor 3x^2 -10x + 2 (over the rationals)

Answer 13

oh, I should have paid more attention then!

Answer 14

Thank you!

Answer 15

you're welcome

Answer 16

Could it also be called the quadratic formula because I can't use that again

Answer 17

Rule:

if d = b^2 - 4ac is a positive perfect square, then you can factor ax^2 + bx + c over the rationals

if d = 0, then ax^2 + bx + c is a perfect square trinomial

Answer 18

why can't you use it?

Answer 19

I used it already; I can't use the quadratic formula (if that's what that is?)

Answer 20

again

Answer 21

you can use the quadratic formula to solve any quadratic equation

3x^2 -10x + 2 = 0 is a quadratic since the leading term has an x^2 in it

so you plug a = 3, b = -10 and c = 2 into the quadratic formula to solve 3x^2 -10x + 2 = 0

Answer 22

I know, but the question asks specifically to use a method of solving different than the one before (I used quadratic formula already)

Answer 23

ok, you can complete the square then

Answer 24

ok

Answer 25

do you know how to do so?

Answer 26

I think I can do that

Answer 27

alright

Answer 28

Thank you so much! Also, do you get any reward for helping people? or is this just your hobby?

Answer 29

just a fun thing to do

Answer 30

hmm cool, thanks!

Answer 31

np