(5)

Let, f(x) = x 5 - 20x 3 + 50x + 2

Now differentiating the function /(#) with respect to x we get,

f'(x) = 5x 4 -60x 2 + 50

f(x) = 5(x 4 -12x 2 +10)

Now equating f'(x) = 0 we get,

x 4 – 12x 2 + 10 = 0

Now finding the nature of function at integer value near by above value we get,

f(0)= 2, f(a)> 0, f(b)< 0, f(-1)< 0 & f(-2)> 0

Now plotting the graph by observing above values, we get,

Hence, it will cross x-axis 5 times.

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