Respuesta :
Answer:
[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]
Step-by-step explanation:
[tex]f\left(x\right)\:=\:2x^2\:+\:16x\:-\:9[/tex]
- Given
[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]
By definition of zeros of a function, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .
What is 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.
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}-4ab } }{2a}[/tex]
This case
The quadratic function is f(x) = 2x² + 16x – 9
Being:
- a= 2
- b=16
- c=-9
the zeros or roots are calculated as:
[tex]x1=\frac{-16+\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]
[tex]x1=\frac{-16+\sqrt{256 +72 } }{4}[/tex]
[tex]x1=\frac{-16+\sqrt{328} }{4}[/tex]
[tex]x1=\frac{-16+\sqrt{4x82} }{4}[/tex]
[tex]x1=\frac{-16+2\sqrt{82} }{4}[/tex]
[tex]x1=\frac{-16}{4}+\frac{2\sqrt{82}}{4}[/tex]
[tex]x1=-4+\frac{\sqrt{82}}{2}[/tex]
and
[tex]x2=\frac{-16-\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]
[tex]x2=\frac{-16-\sqrt{256 +72 } }{4}[/tex]
[tex]x2=\frac{-16-\sqrt{328} }{4}[/tex]
[tex]x2=\frac{-16-\sqrt{4x82} }{4}[/tex]
[tex]x2=\frac{-16-2\sqrt{82} }{4}[/tex]
[tex]x2=\frac{-16}{4}-\frac{2\sqrt{82}}{4}[/tex]
[tex]x2=-4-\frac{\sqrt{82}}{2}[/tex]
Finally, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .
Learn more about the zeros of a quadratic function:
brainly.com/question/842305
