Question

Need help with this one find a plylnominal p(x), with zeros -1,3 such that P(4) = 10

Answer 1

\[reqd. ~polynomial~ is ~P(x)=\left( x+1 \right)\left( x-3 \right)\left( x-4 \right)\]
simplify it.

Answer 2

So the signs switch and p(4) is actually part of the factor and not the degree of the polynomial ?

Answer 3

if f(x1)=0,then x-x1 is a factor of f(x)

Answer 4

it is apart of degree of polynomial as well.

Answer 5

i am wrong ,i thought it is P(4)=0

Answer 6

there should not be factor of x-4
.it should be P(x)=a(x+1)(x-3)

Answer 7

find a by using p(4)=10

Answer 8

Alright for this type of problem ...it is important to remember that *anything times a polynomial will make the polynomial still have the same intercepts

Hence...when you are given the zeros of a polynomial...you can write it out as surjithayer has...as

f(x) = (x + 1)(x - 3)

But you can also write it as

f(x) = C(x + 1)(x - 3)

Because that 'c' wont change anything in terms of intercepts

So you would multiply those out to get

f(x) = C(x^2 - 2x - 3)

That 'C' will help us solving for the P(4) = 10


So now we plug in 4 for the 'x' and make it equal 10

C(4^2 - 2(4) - 3) = 10

C(16 - 8 - 3) = 10

C(5) = 10

C = 2


Now...if C = 2...we can multiply that through the polynomial we had before

f(x) = C(x^2 - 2x - 3)

Will now become

f(x) = 2(x^2 - 2x - 3)

f(x) = 2x^2 - 4x - 6)

Answer 9

P(4)=a(4+1)(4-3)=10
5a=10
a=10/5=2
P(x)=2(x+1)(x-3)

Answer 10

Thanks for the help you guys rock!

Answer 11

you are welcome.Sorry for inconvenience.