In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

$x1,x2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

The quadratic function is f(x) = x² + 4x +9

Being:

a= 1
b= 4
c= 9

the zeros or roots are calculated as:

$x1=\frac{-4+\sqrt{4^{2}-4x1x9 } }{2x1}$

$x1=\frac{-4+\sqrt{16-36 } }{2x1}$

$x1=\frac{-4+\sqrt{-20 } }{2x1}$

and

$x2=\frac{-4-\sqrt{4^{2}-4x1x9 } }{2x1}$

$x2=\frac{-4-\sqrt{16-36 } }{2x1}$

$x2=\frac{-4-\sqrt{-20} }{2x1}$

If the content of the root is negative, the root will have no solution within the set of real numbers. Then $\sqrt{-20}$ has no solution.

Finally, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.

Learn more about the zeros of a quadratic function:

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