Question

Find a cubic function with the given zeros.


`√(5), - √(5) , -7`


f(x) =
`x^(3) - 7x^(2) - 5x - 35`

f(x) =
`x^(3) + 7x^(2) - 5x + 35`

f(x) =
`x^(3) + 7x^(2) - 5x - 35`

f(x) =
`x^(3) + 7x^(2) + 5x - 35`

Answer 1

The third: f(x) = x³ + 7x² - 5x - 35

Explanation:

`f(x)=(x-\sqrt5)(x+\sqrt5)(x+7)\\\\f(x)=(x^2+x\sqrt5-x\sqrt5-(\sqrt5)^2)(x+7)\\\\f(x)=(x^2-5)(x+7)\\\\f(x)=x^3+7x^2-5x-35`

Answer 2

• C. f(x) = x³ + 7x² - 5x - 35

Explanation:

Given zeros of cubic function:

• √5, -√5 and -7

The cubic function has standard form:

• f(x) = ax³ + bx² + cx + d

Without multiplying lets find the value of a, b, c and d:

• a = 1 as all the answer options

Sum of the roots

• -b/a = √5 - √5 - 7 = -7, so b = 7

Sum of the products of the roots (taken two at a time)

• c/a = √5*(-√5) + √5*(-7) + (-√5)(-7) = - 5, so c = -5

Product of the roots

• - d/a = √5*(-√5)*(-7) = 35, so d = -35

So the cubic function is:

• f(x) = x³ + 7x² - 5x - 35

Correct option is C