Question

The zeros of a polynomial are 3/4 and 1/2. Find the polynomial.

Answer 1

Hint!

you should find the following
(x-3/4)(x-1/2)=0

Answer 2

x^(2) − 10x + 3?

Answer 3

i wouldn't use that although it would certainly work

Answer 4

\((x-\frac{3}{4})\) gives a zero of \(\frac{3}{4}\) but so does
\[(4x-3)\]

Answer 5

would my answer be correct?

Answer 6

no

Answer 7

you have to multiply out the factors that will give zeros at \(\frac{3}{4}\) and \(\frac{1}{2}\)
as i wrote, \((4x-3)\) will give a zero at \(\frac{3}{4}\) because if you set
\[4x-3=0\] you get
\[4x=3\]\[x=\frac{3}{4}\]

Answer 8

now you need the other factor, the one that will give a 0 at \(x=\frac{1}{2}\) so start by thinking "what would i set equal to zero and solve that would give an answer of \(\frac{1}{2}\)?

Answer 9

sorry man im struggling on this one is this correct ?
4x^(2) − 10x + 3

Answer 10

ok one factor is \(4x-3\) what is the other factor?

Answer 11

i will tell you if it is that confusing

Answer 12

(x-2)
and ya i would like to know the answer.

Answer 13

no actually \(x=2=0\iff x=2\) you want \(\frac{1}{2}\) so try \((2x-1)\)

Answer 14

here is another way.
x^2-Sx+p=0
where S is sum of the roots
P =product of the roots
S=3/4+1/2=5/4
P=(3/4)*(1/2)=3/8
so
\[\Large x^2-\frac{5}{4}x+\frac{3}{8}=0\]
simplify it.

Answer 15

if you set
\[2x-1=0\] you get
\[2x=1\]
\[x=\frac{1}{2}\] so the two factors are \((4x-3)\) and \((2x-1)\) and your last job is to multiply
\[(4x-3)(2x-1)\]

Answer 16

8x2 -10x +3

Answer 17

yes

Answer 18

thats the one!

Answer 19

whew
hopefully now that you have seen it it will not be so hard in the future right?

Answer 20

right thanks alot.

Answer 21

if one zero is \(\frac{5}{7}\) we can say one factor is \((7x-5)\)

Answer 22

yw

Answer 23

hey can you help me with one more

Answer 24

a different type of
problem though

Answer 25

sure go ahead
ok then post in a new thread, better that way

Answer 26

solve for w.