Answer:
The value of k must be less than 25
Step-by-step explanation:
we have
[tex]f(x)=x^2+10x+k[/tex]
we know that
If the discriminant of a quadratic function is greater than zero, then the function has two distinct zeros
so
The discriminant D is equal to
[tex]D=b^2-4ac[/tex]
we have
[tex]a=1\\b=10\\c=k[/tex]
[tex]D=10^2-4(1)(k)\\D=100-4k[/tex]
Remember that
[tex]D> 0[/tex]
so
[tex]100-4k> 0[/tex]
solve for k
[tex]-4k> -100[/tex]
Divide by -4 both sides
[tex]k< 25[/tex]
therefore
The value of k must be less than 25
