Question

( f(0)=4 )
( Rightarrow a(0)^{2}+b(0)+c=4 )
( Rightarrow quad E=4 )
( f(x)=a x^{2}+b x+4 )
( x+1 ) will be the factor of ( f(x)-4 ) ( Rightarrow quad x=-1 ) will be rout of ( f(x)-4 )
( Rightarrow quad a(-1)^{2}+b(-1)+4-4=0 )
( Rightarrow quad a-b=0 quad Rightarrow a=b )
( x+2 ) will be the fator of ( f(x)-6 )
( Rightarrow x=-2 ) will ( b x ) root of ( f(x)-6 )
( Rightarrow quad a(-2)^{2}+b(-2)+4-6=0 )
( Rightarrow quad 4 a-2 b=2 )
( Rightarrow quad 2 a-b=1 )
( Rightarrow quad a=b=1 )
( Rightarrow a=1, b=1, c=4 )

# 14. Consider a polynomial, f(x) = ax2 + bx + C such that f(0) = 4. When f(x) is divided by x + 1, then the remainder is 4. Also, when it is divided by X + 2, then the remainder is 6. Then value of a, b,

Solution