Question

Which of the following represents the zeros of f(x) = 4x3 − 13x2 − 37x + 10? 5, −2, −1 over 4 5, −2, 1 over 4 5, 2, −1 over 4 5, 2, 1 over 4

Answer 1

The 3 zeros are 5,-2, 1/4

Answer 2

The three zeros are 5 , -2 and
`(1)/(4)`. The second option is correct.

Explanation:

The given polynomial is,

`f(x)=4x^3-13x^2-37x+10`

Use hit and trial method, Put x=-2

`f(x)=4(-2)^3-13(-2)^2-37(-2)+10=0`

Since the value of function is 0 at x=-2 therefore (x+2) is a factor of the given polynomial.

Divide the given polynomial by using synthetic division or long division.

`f(x)=(x+2)(4x^2-21x+5)`

Use grouping method to find the factors,

`f(x)=(x+2)(4x^2-20x-1x+5)`

`f(x)=(x+2)(4x(x-5)-(x-5))`

`f(x)=(x+2)(x-5)(4x-1)`

Equate each factor equal to 0.

`x=-2,5,(1)/(4)`

Therefore, the three zeros are 5 , -2 and
`(1)/(4)`. The second option is correct.