Question

find all the zeros of p (x) = x cube +13x square + 32x+20. if one of its zero is -2​

Answer 1

Answer:

The zeros are -1, -2 and -10.

Step-by-step explanation:

Check first that -2 really is a zero of p(x)!

p(-2) = (-2)³ + 13(-2)² + 32(-2) + 20 = -8 + 52 - 64 + 20 = 0

Good!

Since -2 is a root of p(x), it follows that (x+2) is a factor.  Dividing by (x+2):

p(x) = x³ + 13x² + 32x + 20 = ( x + 2 ) ( x² + 11x + 10 )

Factorizing the quadratic factor:

p(x) = ( x + 2 ) ( x² + 11x + 10 ) = ( x + 2 ) ( x + 1 ) ( x + 10 )

Therefore the other zeros are -1 and -10.