Question

If the product (2x + 3)(x + k) is 2x2 + 13x + 15, what is the value of k?

Answer 1

Given:

The product
`(2x + 3)(x + k)` is
`2x^2+13x+15`.

To find:

The value of k.

Solution:

According to the question,

`(2x + 3)(x + k)=2x^2+13x+15`

Using distributive property, we get

`2x^2+2xk+3x+3k=2x^2+13x+15`

`2x^2+(2k+3)x+3k=2x^2+13x+15`

On comparing both sides, we get

`3k=15\text{ and }2k+3=13`

`k=(15)/(3)\text{ and }2k=13-3`

`k=5\text{ and }2k=10`

`k=5\text{ and }k=5`

Both value of k are same, i.e., 5.

Therefore, the value of k is 5.