What are the zeros of $f (x) = - 4 x^{5} + 3$ $f(x)= −4x^5 + 3$ ?

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What are the zeros of $f (x) = - 4 x^{5} + 3$ $f(x)= −4x^5 + 3$ ?

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Answer 1 · 2015-02-02T20:31:12

The answer is: $x = \frac{24^{\frac{1}{5}}}{2}$ $x=24^(1/5)/2$ .

It is sufficient to solve the system between the function and the line $y = 0$ $y=0$ (x-axis).

So:

$- 4 x^{5} + 3 = 0 \Rightarrow x^{5} = \frac{3}{4} \Rightarrow x = {(\frac{3}{4})}^{\frac{1}{5}} = \frac{3^{\frac{1}{5}}}{2^{\frac{2}{5}}} =$ $-4x^5+3=0rArrx^5=3/4rArrx=""(3/4)^(1/5)=3^(1/5)/2^(2/5)=$
$= \frac{3^{\frac{1}{5}}}{2^{\frac{2}{5}}} \cdot \frac{2^{\frac{3}{5}}}{2^{\frac{3}{5}}} = \frac{{(3 \cdot 2^{3})}^{\frac{1}{5}}}{2} = \frac{24^{\frac{1}{5}}}{2}$ $=3^(1/5)/2^(2/5)*2^(3/5)/2^(3/5)=(3*2^3)^(1/5)/2=24^(1/5)/2$ .

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What are the zeros of $f (x) = - 4 x^{5} + 3$ $f(x)= −4x^5 + 3$ ?

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