1.

When a polynomial `p(x)` of degree 3 is divided by `3x^2-8x+5` quotient and remainder obtained are linear polynomial such that `p(1)=19` and `p(5/3)=25`. So,find the remainder polynomial.

Answer» `f(x)=(3x^2-8x+5)(ax+b)+(c+d)`
Put x=1
`p(1)=(3*1-8+5)(a+b)c+d=19`
`c+d=19-(1)`
Put x=-5/3
`p(5/3)=(3*25/9-8*5/3+5)(a5/3+b)+(c*5/3+d)=25`
`(-5+5)(5/3a+b)+(5/3c+d)=25`
`5/3C+d=25`
`5C+3d=75-(2)`
subtracting equation 1 from equation 2
`2C=18`
`c=9`
`c+d=19`
`9+d=19`
`d=10`
Remainder=cx+d=9x+10.


Discussion

No Comment Found

Related InterviewSolutions