Problem: Find all the real zeros of the polynomial. Use the quadratic formula if necessary.
P(x)= x^3 + 4x^2 + 3x -2
To get the possible zeros of the polynomials p/q can help us, where p= 2
it is the last term. q = 1, this is the coefficient of the first term
We will factor p and q
p = 1*2 and -1*-2
= 1, 2, -1, -2
q = 1*1 and -1*-1
= 1, -1
possible zeros p/q are 1, -1, 2, -2
Test using synthetic division which among them are the real zeros of the polynomial
1 | 1 4 3 -2
1 5 8
_______________________
1 5 8 6 --- > not a real zero
-1 | 1 4 3 -2
-1 -3 0
_____________________
1 3 0 -2 ==> Not a real zero
2 | 1 4 3 -2
2 12 30
_____________________
1 6 15 28 ====> not a real zero
-2 | 1 4 3 -2
-2 -4 2
_________________
1 2 -1 0 ===> a Real zero
the factor now is (x + 2) (x^2 + 2x - 1)
|
--> we can use quadratic formula to get the factor for this where a = 1, b = 2 and c = -2
There are 3 real zeros of the polynomial
x= -2,
,
Rmromero
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