# How do you find the x and y intercepts for #f(x) = pi(x)^5 + pi(x)^4 + sqrt{3}(x) + 1#?

##### 1 Answer

#### Explanation:

The

The

Since all of the coefficients of

#f(-1) = -pi + pi -sqrt(3) + 1 = 1 - sqrt(3) < 0#

#f(0) = 1 > 0#

So the root lies somewhere in

It is extremely difficult to find algebraically, but we can approximate using Newton's method.

Let our first approximation be

#a_(i+1) = a_i - f(a_i)/(f'(a_i))#

#f'(x) = 5pix^4+4pix^3+sqrt(3)#

Putting these formulae into a spreadsheet, I got:

#a_0 = -0.5#

#a_1 = -0.70310491938#

#a_2 = -0.71152815904#

#a_3 = -0.71143261702#

#a_4 = -0.71443260387#

#a_5 = -0.71443260387#