# How do you find all the zeros of #P(x) = 4x^3 - 5x^2 + 3x - 10#?

##### 1 Answer

#### Answer:

The only Real root I could find is at (approximately)

Perhaps the complex roots could be approximated by using the quadratic formula on

#### Explanation:

Based on the graph of this function, we can see that there is only one Real root:

graph{4x^3-5x^2+3x-10 [-18.24, 46.7, -29.57, 2.9]}

We could attempt to use the Rational Root Theorem and test

but as demonstrated in the table below, none of these work:

As a final attempt I used the following code to apply the Newton Method which gave the approximation shown above:

'Newton.Bas

' using the Newton method to approximate root

' of 4x^3-5x^2+3x-10

' Alan P./March 2016lo = 5/4

hi = 2while (hi-lo) > 0.0001

mid = (lo+hi)/2

if P(mid) < 0 then

lo = mid

else

hi = mid

end if

wendprint "At x= "; mid; " P(x)= ";P(mid)

print " (Alt-F4) to end"function P(x)

P=4x^3-5x^2+3*x-10

end function