Question

find all the roots and check your answer.
x^2 + 5x - 14 = 0

Answer 1

Do you know how to do trinomial factoring?

Answer 2

is that with the formula x^2 + bx + c?

Answer 3

No. For example, you can factor x^2-9x+20 to be (x-4)(x-5). Can you figure out how to factor x^2+5x-14 in the same way?

Answer 4

okay I think I understand now because 5*4 = 20 and 5+4=9

Answer 5

Yes, so you want to find two numbers that multiply to get -14 and add to get 5

Answer 6

okay thank you so much

Answer 7

Wait you're not done yet! First write it in factored form.

Answer 8

o okay I know the numbers will be 7 and 2

(x+2) (x-5)

Answer 9

But you used 2 and 5 :P 7 and 2 is correct, try again!

Answer 10

i meant 2,7 that's what i wrote on my problem sorry

Answer 11

(x-2) (x+7)

Answer 12

Perfect, very good. So a root of an equation means when it equals 0. So now you want to solve: (x-2)(x+7)=0. If either (x-2) OR (x-7) is 0, then the whole thing will equal 0. So you can now write it as two equations and solve them independently:

x-2=0
x+7=0

Answer 13

so x = 2 and x = 7

Answer 14

-7

Answer 15

Bravo! That's it! So that's how you solve for the roots of a quadratic equation :)

If you can't factor it, you have to use the "quadratic formula" but I'm not sure you've learned it yet.

Answer 16

thank you