How do you find all the zeros of $F (x) = 9 x^{4} - 37 x^{2} + 4$ $F(x) = 9x^4 - 37x^2 + 4$ ?

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How do you find all the zeros of $F (x) = 9 x^{4} - 37 x^{2} + 4$ $F(x) = 9x^4 - 37x^2 + 4$ ?

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Answer 1 · 2016-02-28T14:28:31

The zeroes are $\frac{1}{3}, - \frac{1}{3}, 2, - 2$ $1/3,-1/3,2,-2$

Explanation:

We notice that

$F (x) = 9 x^{4} - 37 x^{2} + 4 = 9 x^{4} - 36 x^{2} + 4 - x^{2} = 9 x^{2} (x^{2} - 4) - (x^{2} - 4) = (9 x^{2} - 1) (x^{2} - 4) = (3 x - 1) \cdot (3 x + 1) (x + 2) (x - 2)$ $F(x)=9x^4-37x^2+4=9x^4-36x^2+4-x^2= 9x^2(x^2-4)-(x^2-4)=(9x^2-1)(x^2-4)= (3x-1)*(3x+1)(x+2)(x-2)$

Hence the zeroes are the values for which

$F (x) = 0 \Rightarrow (3 x - 1) (3 x + 1) (x + 2) (x - 2) = 0$ $F(x)=0=>(3x-1)(3x+1)(x+2)(x-2)=0$

which are $x_{1} = \frac{1}{3}, x_{2} = - \frac{1}{3}, x_{3} = 2, x_{4} = - 2$ $x_1=1/3,x_2=-1/3,x_3=2,x_4=-2$

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How do you find all the zeros of $F (x) = 9 x^{4} - 37 x^{2} + 4$ $F(x) = 9x^4 - 37x^2 + 4$ ?

1 Answer

Explanation:

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How do you find all the zeros of F(x)=9x4−37x2+4F(x) = 9x^4 - 37x^2 + 4?

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How do you find all the zeros of $F (x) = 9 x^{4} - 37 x^{2} + 4$ $F(x) = 9x^4 - 37x^2 + 4$ ?