Find the zeros of the function algebraically.
f(x) = 16x4 − 49x2

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Step-by-step explanation:

Just Simply Use Identity:

  a^2 - b^2 = ( a+b) ( a-b)

   Then:

     ( 49X^4 - 36 X^2) = 0

       (7 X^2 + 6 X) ( 7X^2 - 6X) =0

       7X^2 + 6X = 0, then           X( 7X +6) =0    X=0,  7x +6 =0   X = -6/7

           7X^2 -6x =0                   X( 7x - 6) =0   X =0   7x -6 =0    X =6/7

Pull out a factor of x² from f(x) :

16x⁴ - 49x² = x² (16x² - 49)

Now write it as a difference of squares, then factorize:

16x⁴ - 49x² = x² ((4x)² - 7²)

16x⁴ - 49x² = x² (4x - 7) (4x + 7)

Set this equal to 0 and solve for x :

x² (4x - 7) (4x + 7) = 0

x² = 0   or   4x - 7 = 0   or   4x + 7 = 0

x = 0   or   x = 7/4   or   x = -7/4