Question

If the graph of f(x)= x^2+10x+k has two distinct zeros, find the value of k

Answer 1

Answer:

The value of k must be less than 25

Step-by-step explanation:

we have

$f(x)=x^2+10x+k$

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

$D=b^2-4ac$

we have

$a=1\\b=10\\c=k$

$D=10^2-4(1)(k)\\D=100-4k$

Remember  that

$D> 0$

so

$100-4k> 0$

solve for k

$-4k> -100$

Divide by -4 both sides

$k< 25$

therefore

The value of k must be less than 25