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What are the zeros of the quadratic function f(x) = 6x2 – 24x + 1?

A) x = –2 + square root 1/2 or x = –2 – square root 1/2

B) x = 2 + square root 1/2 or x = 2 – square root 1/2

C) x = –2 + square root 23/6 or x = –2 – square root 23/6

D) x = 2 + square root 23/6 or x = 2 – square root 23/6

Respuesta :

Answer:

Option D. [tex]x=2+\sqrt{\frac{23}{6}},2-\sqrt{\frac{23}{6}}[/tex]

Step-by-step explanation:

The given function is f(x) = 6x² - 24x + 1

The zeros of the given quadratic function can be calculated by quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

By putting values a = 6, b = -24, c = 1 in the quadratic formula

[tex]x=\frac{24\pm \sqrt{(-24))^{2}-4(6)(1)}}{2(6)}=\frac{24\pm \sqrt{576-24}}{12}=\frac{24\pm \sqrt{552}}{12}=2\pm \sqrt{\frac{552}{144}}=2\pm \sqrt{\frac{23}{6}}[/tex]

[tex]x=(2+\sqrt{\frac{23}{6}}),(2-\sqrt{\frac{23}{6}})[/tex]

Option D. is the correct option.

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