Question

t^2 - 3t - 10 = 0

help?

Answer 1

Find two numbers which multiply to -10 AND add to -3

Answer 2

Which two numbers do this?

Answer 3

-5 & 2

Answer 4

good, so the left side factors to (t-5)(t+2)

Answer 5

therefore

t^2 - 3t - 10 = 0

turns into

(t-5)(t+2) = 0

Answer 6

what's next?

Answer 7

t -5 = 0 = 5

t + 2 = 0 = -2

Answer 8

perfect, so the solutions are t = 5 or t = -2

Answer 9

okay thanks! and what about; 1/2x^2 - 3x - 8 = 0

Answer 10

this one is a bit different because of the leading coefficient (or the first coefficient) of 1/2. But we can easily fix this by multiply EVERY term by 2 to clear out that fraction


So multiply 1/2x^2 by 2 to get 2*(1/2x^2 ) = x^2

multiply -3x by 2 to get 2*(-3x) = -6x

and multiply -8 by 2 to get 2*(-8) = -16


This means that

1/2x^2 - 3x - 8 = 0

turns into

x^2 - 6x - 16 = 0

Answer 11

Now we must find two numbers that both multiply to -16 AND add to -6, and they are...?

Answer 12

-8 & 2

Answer 13

good, so

x^2 - 6x - 16 = 0

becomes

(x-8)(x+2) = 0

which means x is??

Answer 14

8 & -2?

Answer 15

you got it, does the whole process make sense?

Answer 16

yes, but then i checked with only # 8 like (8-8)(8+2) and i also got 0

Answer 17

that's exactly right, if you check -2 you'll get the same result as well

Answer 18

ohh! okk:)

Answer 19

thanks!

Answer 20

you're welcome

Answer 21

one more thing

Answer 22

what's that

Answer 23

also my teacher gave me this formula; b^2 - 4ac

Answer 24

how do i use it?

Answer 25

that's the discriminant

Answer 26

it will allow you to determine the number and type of solutions that a quadratic equation will have

Answer 27

it will also determine whether you can factor or not

Answer 28

can you do an example from the last problem? or; 2x^2 - 4x +1 = 0

Answer 29

sure thing

Answer 30

ok:)

Answer 31

let's say we want to find the number and type of solutions to x^2 - 6x - 16 = 0


In the case of x^2 - 6x - 16 , it's in the form ax^2+bx+c where a = 1, b = -6 and c = -16


Plug these values into b^2 - 4ac and simplify


b^2 - 4ac

(-6)^2 - 4(1)(-16)

36 - 4(1)(-16)

36 - 4(-16)

36 + 64

100

Because we got a positive number, we know that there are two real solutions (that are distinct/different)

Because we got a perfect square (100 = 10^2), we know that these two solutions are rational (or fractional) solutions.

Furthermore, since we got a perfect square, we know that x^2 - 6x - 16 can be factored. If we didn't get a perfect square, then we would automatically know that it couldn't be factored, which would save us time.

Answer 32

Does that make sense?

Answer 33

ohh okay thank you! :)

Answer 34

sure thing :)