1.

write the coefficient of `x^(2)` in each of the following (i) `(pi)/(6)x+x^(2)-1` (ii) 3x-5 (iii) `(x-1)(3x-4)` (iv) `(2x-5)(2x^(2)-3x+1)`

Answer» (i) the coefficient of `x^(2) "in " (pi)/(6) x+x^(2)-1 "is" 0.`
(ii) the coeficient of `x^(2) ` in `3x-5 "is "0.`
(iii) Let `p(x)=(x-1)(3x-4)`
`=3x^(2)-7x+4`
`=3x^(2)-4x-3x+4`
hence , the coefficient of `x^(2)` in p(x) is 3.
(iv) Let p(X) `=(2x-5)(2x^(2)-3x+1)`
`=x(2x^(2)-3x+1)-5(2x^(2)-3x+1)`
`=4x^(3)-6x^(2)+2x-10x^(2)+15x-5`
`=4x^(3) -16x^(2) +17x-5`
Hence , the coefficient of `x^(2)` in p(x) is -16.


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