Math zero's problem

Question

How would you find all the zeroes for x^3+4x^2+4x+1?

Answer 1

Hi Andre,

 

As Kenneth suggested, doing synthetic division, you end up with the polynomial

x²+3x+1

 

According to the quadratic formula, this polynomial has two real roots.

Remember: discriminant, i.e., sqrt(b²-4ac) is greater than 1.

 

Use the quadratic formula, (-b +- sqrt(b²-4ac)) / (2a) 

where a=1, b=3 and c=1  you should get the roots of the polynomial as

(-3+sqrt(5))/2  and  (-3-sqrt(5))/2 

 

Then, the roots of the polynomial x^3+4x^2+4x+1 are

((-3-sqrt(5))/2, -1, (-3+sqrt(5))/2)

 

Answer 2

There are no positive Real roots, according to Descartes rule.

-1 is a zero (see byinspection).

Do synthetic division to get depressed polynomial.

Proceed from there, using techniques taught in Algebra II class.