Question

if the polynomial p x is equal to 3 x cube minus 2 x square + x + 1 then coefficient of the x cube is​

Answer 1

Step-by-step explanation:

Given p(x)=x³-2x²-5x+6

p(3)=27-18-15+6=0

p(-2)=-8-8+10+6=0

p(1)=1-2-5+6=0

Hence the given numbers are the zeroes of the given cubic polynomial.

Let the coefficients be q,r,s,t and roots a,b,c

Relation between roots

sum of the roots=a+b+c=-r/q=-(-2/1)=2=3+(-2)+1

product of the roots=abc=-t/q=-6=3×-2×1

sum of the products of pair of roots=ab+bc+ca=s/q=-5=3(-2)+(-2)1+1(3)