Question

( f(x)=x^{4}+p x^{3}+2 x^{2}-3 x+q )
( x^{2}-1 ) is factor & ( f(x) )
( Rightarrow(x-1)(x+1) ) is a fator ( delta quad(x) )
( Rightarrow quad x=1, x=-1 ) are roots of ( f(x) )
( Rightarrow f(1)=0 quad & quad f(-1)=0 )
( Rightarrow quad 1+p+2-3+q=0 quad & quad 1-p+2+3+q=0 )
( Rightarrow quad p+q=0 quad 8 quad p-q=6 )
( Rightarrow quad 2 p=6 Rightarrow p=3 )
( Rightarrow quad q=-3 )
Hence, ( quad b=3 ) and ( q=-3 )

# 20. Find the values of p and a so that x+px+2x2-3x+q is divisible by (-1)

Solution