# Pre calculus

posted by Steve

Find all roots
f(x)- x^3+2x^2-15x+30
Factor f(x) completely.

I can't find any roots and always get a remainder with 1, -1, 2, -2

What do you do if you cannot find a root??
Using Calc button on ti84 I got
X= -5.619 Y=1.4E-11

Still can't find zeros...

1. Steve

Assuming you meant that - sign at the front,

-x^3+2x^2-15x+30
= -x^2(x-2) -15(x-2)
= -(x-2)(x^2+15)

If you did mean x^3+2x^2-15x+30
then there are no rational roots, and you have to fall back on numerical methods, like bisection or Horner's method.

2. Steve

sorry it was f(x)= not (-)

I got no real roots either

3. Steve 2.0

well, there is always at least one real root for a cubic. Just not always rational.

Since
f(-6) = -24
f(-5) = 30

you know there is a root inside (-6,-5). The work comes in narrowing it down a bit more.

4. Steve

Can you show me the steps or is this just on calculator?

5. Damon

if it is x^3 + 2 x^2 - 15 x + 20 = 0
then:
http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
gives
x = -5.44
x = 1.72 +/- .853 i

6. Steve 2.0

well, there are lots of methods. An easy one is bisection. Since you know the root is between -6 and -5, try -5.5

f(-5.5) = 6.625
Now you know that the root r is in (-6,-5.5), so try -5.75
f(-5.75) = -7.73
r is in (-5.75,-5.5)
f(-5.625) = -0.322
each time take the midpoint of the interval where f(x) changes sign. It may be slow, but it always works.

7. Steve

thx

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