Question

X³+kx²-10x-15 is divided by (x-3) remainder +7 find k

Answer 1

Question :-

• Find k, if x³+ kx²- 10x - 15 is divided by (x-3), leaves the remainder 7.

Answer

Given :-

• when p(x) = x³+ kx²-10x-15 is divided by g(x) = x-3, it leaves the remainder 7.

To find :-

• Value if k.

Concept used :-

Remainder theorem:

• Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

Solution:-

Since, p(x) = x³+ kx²- 10x - 15

and g(x) = x - 3

Remainder = 7

Now, p(x) is divided by x - 3,

therefore, by remainder theorem,

remainder is p(3)

According to statement,

Remainder = 7

⇛ p(3) = 7

⇛ (3)³+ k(3)²- 10 (3) - 15 = 0

⇛ 27 + 9k - 30 - 15 = 0

⇛ 9k - 18 = 0

⇛9k = 18

⇛ k = 2