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Answer :
Answer:
- C. f(x) = x³ + 7x² - 5x - 35
Step-by-step 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
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Answer:
The third: f(x) = x³ + 7x² - 5x - 35
Step-by-step explanation:
[tex]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[/tex]
