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Find how many roots of the equations x^4...

Find how many roots of the equations `x^4+2x^2-8x+3=0.`

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Let `f(x) = x^(4) + 2x^(2)-8x+3 .`
Then `f'(x) = 4x^(3) + 4x - 8 = 4 (x - 1) (x^(2)+x+2)`
Now `f'(x) = 0 rArr x = 1`
Hence, the graph of y = f(x) has only one ture (maxima/minima).
Now `f(1) = 1 + 2 - 8 + 3 lt 0`
Also when x `topminfty,f(x)toinfty`
Then the graph of the function is as shown in the figure.

Hence, equation f(x) = 0 has only two real roots
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