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

Answer:

The three zeros are 5 , -2 and $\frac{1}{4}$. The second option is correct.

Step-by-step 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.

$x=-2,5,\frac{1}{4}$

Therefore, the  three zeros are 5 , -2 and $\frac{1}{4}$. The second option is correct.