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The remainder when P(x) = 2x^2-x-6 is di...

The remainder when P(x) = `2x^2-x-6` is divided by (x-2) is equal to :

Text Solution

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By Remainder theorem `f(a)=a,f(b)=b` and `f(c)=c`
Let the quotient be `Q(x)` and remainder is `R(x)`.
`:.f(x)=(x-a)(x-b)(x-c)Q(x)+R(x)`
`:.f(a)=0+R(a)impliesR(a)=a`
`f(b)=0+R(b)impliesR(b)=b` and `f(c)=0+R(c)`
`impliesR(c)=c` ltbr. So the equation `R(x)-x=0` has there roots a,b and c. But its degree is atmost two. So `R(x)-x` must be zero polynomial (or identity)
Hence `R(x)=x`.
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