Question

Obtain the other zeroes of the polynomial p(x)= x + 2x3 - 7x2 - 8x + 12
if two of its zeroes are (-2) and (-3).​

Answer 1

Step-by-step explanation:

product of roots=12

−1×2×α×β=12

αβ=−6

sum of the roots=2

α+β−1+2=2

α+β=1

β=−

α

6

α−

α

6

=1

α

2

−6=α

α

2

−α−6=0

α

2

−3α+2α−6=0

α(α−3)+2(α−3)=0

(α+2)(α−3)=0

α=3,−2