14. Consider a polynomial, f(x) = a...
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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,

11th - 12th Class
Maths
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( 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 )
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