High School

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------------------------------------------------ Find a cubic function with the given zeros.


[tex]\sqrt{5}, - \sqrt{5} , -7[/tex]


f(x) = [tex]x^{3} - 7x^{2} - 5x - 35[/tex]

f(x) = [tex]x^{3} + 7x^{2} - 5x + 35[/tex]

f(x) = [tex]x^{3} + 7x^{2} - 5x - 35[/tex]

f(x) = [tex]x^{3} + 7x^{2} + 5x - 35[/tex]

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

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]

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