Considering the way of solve a quadratic function, the quadratic function f(x) = -4x² + 2x -5 does not have zeros o roots.
Solving a quadratic function involves finding the zeros of the function, this is, the points where a polynomial function crosses the axis of the independent term (x).
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:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
The quadratic function is f(x) = -4x² + 2x -5
Being:
the zeros or roots are calculated as:
[tex]x1=\frac{-2+\sqrt{2^{2}-4x(-4)x(-5) } }{2x(-4)}[/tex]
[tex]x1=\frac{-2+\sqrt{4-80} }{2x(-4)}[/tex]
[tex]x1=\frac{-2+\sqrt{-76} }{2x(-4)}[/tex]
and
[tex]x2=\frac{-2-\sqrt{2^{2}-4x(-4)x(-5) } }{2x(-4)}[/tex]
[tex]x2=\frac{-2-\sqrt{4-80} }{2x(-4)}[/tex]
[tex]x2=\frac{-2-\sqrt{-76} }{2x(-4)}[/tex]
As the √-76 has no real solution (it is not possible to calculate it), it indicates that it is not possible to calculate the roots of the function
Finally, the quadratic function f(x) = -4x² + 2x -5 does not have zeros o roots.
Learn more about the zeros of a quadratic function:
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