Question

If p(x) =x3+kx2+hx+6and (x+1) and (x-2) are factor of p(x) then find the value of h and k

Answer 1

given (x+1) is a factor of p(x)

from (x+1) we get ,

X=-1

now substituting the value of x= -1 in p(x) we get,

p(-1) = (-1)*3 + k(-1)*2+ h*-1 +6

by factor theorem...

0= 5+k -h

or, k-h = -5............(i)

similarly , it is given that (x-2) is a factor of p(x)

so from (x-2) we get x= 2

by substituting x=2 in p(x) we get,

p(2) = (2)*3+k(2)*2 +h(2) + 6

or, by factor theorem,

0= 8+4k+2h+6

or, 4k+2h = -14

or,2(2k+h)= -14

2k+ h= -14/2

or, 2k+h = -7............(ii)

now by adding (i) and (ii) we get...

k-h = -5

2k+h=-7

________________

3k = -12

or, k = -12/3

k= -4 is Ur answer...

now by putting k= -4 in (i) we get,

-4 -h =-5

or, -h = -5+4

or, -h = -1

or,h = 1 is Ur answer..

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