Question

The polynomial (x³+px+q) is completely divisible by (x-1) (x-2) find the value of p and q​

Answer 1

Answer:

p = 7 & q = -8

Step-by-step explanation:

We know that (x-1) (x-2) is divisible by the polynomial (x^3+px+q)

So,

(x-1) & (x-2) are also divisible by the polynomial (x^3+px+q)

So,

1 & 2 can be the two zeroes of the given polynomial

then,

=> 1^3+p(1)+q = 0

=> 1+p+q = 0

=> p+q = -1 ---------(i)

&,

=> 2^3+p(2)+q = 0

=> 8+2p+q = 0

=> 2p+q = -8 ------------(ii)

We got two equations. Now, we can find the values of p & q by many methods such as Substitution, Elimination, Cross multiplication etc.

By substitution method:-

taking eq (i).......

=> p+q = -1

=> q = (-1)+(-p) ----------(iii)

putting eq. (iii) in eq. (ii)

=> 2p+(-1-p) = -8

=> -1-p = -8

=> -p = -8+1

=> -p = -7

=> p = 7

Now,

Putting this value in eq. (iii)

=> q = -1-7

=> q = -8

Hope this will help!!

please tell me if I made a mistake!!