Question

(1) When divided by x - 3 the polynomials x3 – px2 + x + 6 and
2x3 - x2 - (p + 3) x - 6 leave the same remainder. Find the value of 'p.​

Answer 1

Ans:- Given:-

p(x) = x³ + px² + x + 6

p(x) = 2x³ - x² -(p + 3)x - 6

g(x) = x - 3

To find value of p

Solution:-

=> x - 3 = 0

=> x = 3

now, put the value of x in p(x) we get

=> p(3) = (3)³+p(3)²+3+6 = 0

=> p(3) = 27 + 9p + 9 = 0

=> p(3) = 36 + 9p = 0 --------- (1)

now again,put the value of x in p(x) we get,

=> p(3) = 2(3)³-(3)²-(p+3)(4)-6 = 0

=> p(3) = 54 - 9 - 4p + 12 - 6 = 0

=> p(3) = 51 - 4p = 0 ------------ (2)

from (1) and (2) we get

=> 36 + 9p = 51 - 4p (since both are equal to 0)

=> 9p + 4p = 51 - 36

=> 13p = 15

=> p = 15/13

here is your answer

hope it will help you