Question

Help please!

Find the value of k such that -2/3 is a zero of the function f(x) = 4x + k /7.

How do you solve this?

Answer 1

if -2/3 is a zero this function, then it means that \(f(-2/3)=0\).

so just replace \(x\) with \(-2/3\) in the expression for \(f(x)\) and set the while thing equal to zero, then solve to find \(k\).

Answer 2

*whole

Answer 3

\[
f\left(-\frac 23\right)=0\implies 0=4\left(-\frac23\right)+\frac k7
\]This equation allows you to solve for \(k\).

Answer 4

is it -8/3.... i think i might have done something wrong.

Answer 5

please show your steps so that I can spot where you may have made a mistake

Answer 6

hang on, is your equation:\[ f(x) = 4x + \frac{k}{7}\tag{1}\]or,\[f(x)=\frac{4x+k}{7}\tag{2}\]

Answer 7

4 (-2/3) + k /3 = 0. I multiplied 3 on both sides so I got rid of the 3 and made it 4(-2/3) + k = 0. then i solved for 4(-2/3) and ended up with -8/3.

Answer 8

the second one!

Answer 9

you typed:
4 (-2/3) + k /3 = 0.

shouldn't that be:
(4 (-2/3) + k)/7 = 0.

Answer 10

oh you're right. my bad haha! let me try that again.

Answer 11

you should use brackets to avoid ambiguity, so your question should have been typed as:

f(x)=(4x+k)/7

Answer 12

sorry about that :(

Answer 13

np :)

Answer 14

in any case, you will still end up with:

4(-2/3) + k = 0

this then leads to:

-8/3 + k = 0

you then drew the wrong conclusion from this

Answer 15

you need to add 8/3 to both sides of this equation

Answer 16

so it's positive 8/3, right?

Answer 17

yes - well done! :)

Answer 18

thanks so much! appreciate the help :)

Answer 19

yw :)

Answer 20

thank you @wio too! :)