Respuesta :
Answer:
[tex]k=-16,k=-8,k=8,k=16[/tex]
Step-by-step explanation:
We are given quadratic equations as
[tex]x^2+kx+15[/tex]
and it can be factored as
[tex]=(x+a)(x+b)[/tex]
now, we can multiply factor term
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]
now, we can compare
[tex]x^2+(a+b)x+ab=x^2+kx+15[/tex]
so, we get
[tex]k=a+b[/tex]
[tex]ab=15[/tex]
we are given that
'a' and 'b' are integers
so, we can find all possible factors
[tex]15=(-1\times -15),(1\times 15)[/tex]
[tex]15=(-3\times -5),(3\times 5)[/tex]
so, we can find k
At [tex](-1\times -15)[/tex]:
[tex]k=a+b[/tex]
we can plug values
[tex]k=-1-15[/tex]
[tex]k=-16[/tex]
At [tex](1\times 15)[/tex]:
[tex]k=a+b[/tex]
we can plug values
[tex]k=1+15[/tex]
[tex]k=16[/tex]
At [tex](-3\times -5)[/tex]:
[tex]k=a+b[/tex]
we can plug values
[tex]k=-3-5[/tex]
[tex]k=-8[/tex]
At [tex](3\times 5)[/tex]:
[tex]k=a+b[/tex]
we can plug values
[tex]k=3+5[/tex]
[tex]k=8[/tex]
So, values of k are
[tex]k=-16,k=-8,k=8,k=16[/tex]
