Question

Find the zeros of the function f(x)=x^2-2x-2.f(x)=x2−2x−2. Round values to the nearest hundredth (if necessary).

Answer 1

By definition, the zeros of the quadratic function f(x) = x² - 2x - 2 are 2.732 and -0.732.

Zeros of a function

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

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:

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

This case

The quadratic function is f(x) = x² - 2x - 2

Being:

• a= 1
• b= -2
• c= -2

the zeros or roots are calculated as:

$x1=\frac{-(-2)+\sqrt{(-2)^{2} -4x1x(-2)} }{2x1}$

$x1=\frac{2+\sqrt{4 +8} }{2}$

$x1=\frac{2+\sqrt{12} }{2}$

$x1=\frac{2+3.464}{2}$

$x1=\frac{5.464}{2}$

x1= 2.732

and

$x2=\frac{-(-2)-\sqrt{(-2)^{2} -4x1x(-2)} }{2x1}$

$x2=\frac{2-\sqrt{4 +8} }{2}$

$x2=\frac{2-\sqrt{12} }{2}$

$x2=\frac{2-3.464 }{2}$

$x2=\frac{-1.462 }{2}$

x2= -0.732

Finally, the zeros of the quadratic function f(x) = x² - 2x - 2 are 2.732 and -0.732.

Learn more about the zeros of a quadratic function:

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