Question

Which function has zeros at x = −2 and x = 5?

Answer 1

f(x) = x²-3x-10 is the answer.

Explanation:

We have to find the function that has zeros at x = -2 and x=5 .

Function that has two zeros is of the form :

(x-c)(x-d) = 0

If the function has two zeros at x = -2 and x=5 then it is of the form:

(x-(-2))(x-5)=0

(x+2)(x-5) = 0

(x+2)(x-5) = 0

x²-5x+2x-10 =0

x²-3x-10 = 0 is the function has zeros at x = −2 and x = 5.

Answer 2

f(x)=
`x^2-3x-10`

Explanation:

If a function has two zeros x=a and x=b then function can be written as

`(x-a)(x-b)`

similarly if a function has two zeros at x = −2 and x = 5

then function can be written as

`(x+2)(x-5)`

`x^2-5x+2x-10`

`x^2-3x-10`

Therefore f(x)=
`x^2-3x-10` is required function