Considering the definition of zeros of a quadratic function, the zeros of the quadratic function f(x) = 3x² -7 x +1 are [tex]x1=\frac{7+\sqrt{37 } }{6}[/tex] and [tex]x2=\frac{7-\sqrt{37 } }{6}[/tex].
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:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
This case
The quadratic function is f(x) = 3x² -7 x +1
Being:
the zeros or roots are calculated as:
[tex]x1=\frac{-(-7)+\sqrt{(-7)^{2}-4x3x1 } }{2x3}[/tex]
[tex]x1=\frac{7+\sqrt{49-12 } }{6}[/tex]
[tex]x1=\frac{7+\sqrt{37 } }{6}[/tex]
and
[tex]x2=\frac{-(-7)-\sqrt{(-7)^{2}-4x3x1 } }{2x3}[/tex]
[tex]x2=\frac{7-\sqrt{49-12 } }{6}[/tex]
[tex]x2=\frac{7-\sqrt{37 } }{6}[/tex]
Finally, the zeros of the quadratic function f(x) = 3x² -7 x +1 are [tex]x1=\frac{7+\sqrt{37 } }{6}[/tex] and [tex]x2=\frac{7-\sqrt{37 } }{6}[/tex].
Learn more about the zeros of a quadratic function:
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