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

Question

asked Oct 28, 2021 183k views

1 Answer

Bujar · Answer 1 · 2021-11-01T12:23:27+0000

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.