Question

A polynomial p has zeros when x = 5, x = -1, and x = -1/4

What could be the equation of p?
A. p(x) = (x +5)(x + 1)(4x + 1)
B. p(x) = (x - 5)( x + 1)(4x + 1)
C. p(x) = (x + 5)(x - 1)(4x - 1)
D. p(x) = (5x)(-1x)( - 1/4x)

Answer 1

`x=5` ⇒
`(x-5)=0`

`x=-1` ⇒
`(x+1)=0`

`x=-1/4` ⇒
`(x+1/4)=0` ⇒
`(4x+1)=0`

`p(x)=(x-5)(x+1)(4x+1)=0`

`Option(B)`

-------------------------

Hope it helps...

Have a great day!!

Answer 2

p(x) = (x-5) (x+1)(4x+1)

Explanation:

We know the equation for a polynomial with zeros is written as

f(x) = a( x-b1) (x-b2)...... where b are the zeros

We have zeros x = 5, x = -1, and x = -1/4

p(x) = a( x-5) (x- -1) (x - -1/4)

p(x) = a (x-5) (x+1) (x+1/4)

Let a = 4

p(x) = 4 (x-5) (x+1) (x+1/4)

p(x) = (x-5) (x+1)(4x+1)