Question

When the polynomial 2x3+px2+qx+9is divided by x-1, the remainder is 8 and when divided by x-2, the
remainder is 15. Find the values of p and q.

Answer 1

Answer:

p=1

Step-by-step explanation:

The Remainder is same whne (x−3) divides (x3−px2+x+6) & (2x3−x2−(p+3)x−6)

∴ Using Remainder Theorem

R(3)=x3−px2+x+6

          =33−p(32)+3+6

          =27−9p+3

          =36−9p

R(3)=2x3−x2−(p+3)x−6

          =2(33)−32−(p+3)3−6

          =2×27−9−3p−9−6

          =54−24−3p

          =30−3p

Remainder are same

∴36−9p=30−3p

36−30=−3p+9p

6=6p

1=p