Question

f(x) = x^2 + x - 30

what are the zeros of the equation?

Answer 1

@iambatman I don't need the answer, I just need someone to walk me through this step by step cause I know how to get the answer however I don't know how to get there

Answer 2

I know I have to use the quadratic formual. but I don't really understand how to set it up correctly

Answer 3

The zeros are where the thing intersects the x-axis. The place(s) where y=f(x) = 0
set f(x) = 0

0 = x^2 + x - 30

Answer 4

oh okay.

Answer 5

the general form for a quadratic is Ax^2 + Bx + C, where A, B and C are the coefficients on each of the terms, the last being Cx^0

Answer 6

That one you have can be factored pretty easy if you dont want to use the quadratic formula.

0 = (x + )( x - )

Answer 7

a*b = 30
and
a - b = +1

What factors of 30, add together to give +1

Answer 8

I suppose I'm still a bit lost about what exactly to do after I set f(x) to 0

Answer 9

I could easily start guessing at what x is but that doesn't seem right

Answer 10

30 = a*b = 5*6
+1 = a - b = 6 - 5

Answer 11

do I just start plugging in values for x?

Answer 12

You can always use the quadratic formula if you want. This one is easy to factor because the zeroes are whole number integers.

f(x) = (x+6)(x-5)

Answer 13

5*6 is 30 and 6-5 is 1

Answer 14

or you can use the formula in any case
\[x = \frac{ -B \pm \sqrt{B^2 - 4*A*C} }{ 2A }\]

A= 1
B= 1
C = -30

Answer 15

so with the other one I'd say x * x^2 = -30?

Answer 16

The function is
f(x) = x^2 + x - 30

because the coefficient on the x^2 is a 1, you can write...

Answer 17

\[f(X) = (x \pm a)(x \pm b)\]

Answer 18

oh okay

Answer 19

then what do I do?

Answer 20

OHHH I finally got what you were saying uptop

Answer 21

Then you write the factors of 30 down...

30 * 1
6 * 5
2*15
3*10
------------

Think, which of those factors will add or subtract to give you the value of B, in this case B is +1

Answer 22

the factors 6*5 are the ones

6*5 = 30 and 6-5 = 1

Answer 23

x^2 +x - 30 = (x +6)(x-5)

Answer 24

ohhh okay. that makes sense now :)

Answer 25

In any case though, you can use the quadratic formula and get the answer for the zeros...
\[x = \frac{ -B \pm \sqrt{B^2 - 4*A*C} }{ 2A } = \frac{ -1 \pm \sqrt{1 - (4*1*-30)} }{ 2*1 } = \frac{ -1 \pm \sqrt{121} }{ 2 } = \frac{ -1 \pm 11 }{ 2 }\]

Answer 26

\[x=\frac{-1+11 }{ 2 }~~~or~~~x=\frac{ -1-11 }{ 2 }\]

x=5 or x=-6

Answer 27

okay thank you for you help DanJ! :)

Answer 28

Which tells you the factors
(x - 5)(x+6) = 0

Answer 29

(x-5) = 0
or
(x+6) = 0

x=5 or x=-6

Answer 30

you're welcome, anytime