Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Algebra

Can someone tell me what I'm doing wrong here? Long day.

f(x) = 2x² + px + q. Given that f(-3) = 0, and f(4) = 2, find the value of p and q.

f(x) = 2x² + px + q.

f(-3) = 2(-3)² - 3p + q = 0
        = 18 - 3p + q = 0
∴ q = 3p - 18

f(4) = 2(4)² + 4p + q - 2 = 0
      = 30 + 4p + q = 0

substituting the first into the second:

30 + 4p + (3p - 18) = 0
30 + 4p + 3p - 18 = 0
7p = - 12
p = -12/7

I know I haven't given an answer for q... only because my answer for p is wrong. What have I done?

Thanks

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Algebra

Edited by Pi Man:  Ignore this post (#2) .   I made the mistake, not Daniel.   

f(4) = 2(4)² + 4p + q - 2 = 0
      = 30 + 4p + q = 0

f(4) = 2(4)² + 4p + q - 2 = 0
      = 32 + 4p + q = 0                   32, not 30
q = -4p -32

-4p-32 = 3p - 18
-14 = 7p
p = -2

Last edited by pi man (2007-10-22 16:27:28)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Algebra

No, Daniel is right. 2(4²) -2 = 30, like he says.

In fact, everything is right, including the value of p. Be more confident!

---

Why did the vector cross the road?
It wanted to be normal.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Algebra

Whoops.   Sorry about that Daniel.   And thanks, Mathsyperson.  I was a little too hasty.   If I solved it all the way through and then double-checked, I would have seen I was the one who made the mistake

I'll do now what I should have done before.  Continuing with what you already figured out....
p = -12/7  and q = 3p - 18

q = 3(-12/7) - 18
q = -36/7 - 126/7 = -162/7

Plug p and q back into your original question to double-check.

f(x) = 2x² - 12x/7 -162/7
f(-3) = 2(9) + 36/7 - 162/7
        = 18 - 126/7
        = 18 - 18 = 0

f(4) = 2(16) - 48/7 - 162/7
      = 32 - 210/7
      = 32 - 30 = 2

Much better!

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Algebra

Stupid textbook! I waste so much time trying to find where I've gone wrong when actually I haven't!

Thanks!

popo

Member

Registered: 2007-10-21

Posts: 4

Re: Algebra

What was the book?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Algebra

Heinemann AS modular books. The number of errors they make in the answers is ridiculous.