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On dividing x^3-3x^2+x+2 by a polynomial …

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On dividing x^3-3x^2+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4, respectively. Find g (x) . If we put g (x)=0 , find nature of roots g (x)

Posted by Pratham Sharma 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Rakesh Kumar Tiwari 7 years, 3 months ago

x³-3x²+x+2=g(x).(x-2)-2x+4,,,,,,,,,,,, =›x³-3x²+x+2+2x-4=g(x).(x-2),,,,,,, =›x³-3x²+3x-2=g(x).(x-2),,,,,,,,, =›x²(x-2)-x(x-2)+(x-2)=g(x).(x-2),,,,,,,, =›(x-2).(x²-x+1)=g(x).(x-2),,,,,,,,, =›x²-x+1=g(x),,,,,,,, if g(x)=0,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, =›D=b²-4ac,,,,,,,,,,,,,,,,,, =›D=(-1)²-4×1×1=-3<0,,,,,,,, the roots are non real.

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