Given:
The product [tex](2x + 3)(x + k)[/tex] is [tex]2x^2+13x+15[/tex].
To find:
The value of k.
Solution:
According to the question,
[tex](2x + 3)(x + k)=2x^2+13x+15[/tex]
Using distributive property, we get
[tex]2x^2+2xk+3x+3k=2x^2+13x+15[/tex]
[tex]2x^2+(2k+3)x+3k=2x^2+13x+15[/tex]
On comparing both sides, we get
[tex]3k=15\text{ and }2k+3=13[/tex]
[tex]k=\dfrac{15}{3}\text{ and }2k=13-3[/tex]
[tex]k=5\text{ and }2k=10[/tex]
[tex]k=5\text{ and }k=5[/tex]
Both value of k are same, i.e., 5.
Therefore, the value of k is 5.
