Considering the definition of function quadratic and roots, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.
Function quadratic
The function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
Definition of roots
The roots are those values of x for which the expression is 0, so it graphically cuts the x-axis.
This can be solved by:
[tex]x1, x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
x-intercepts of f(x) = x² + 5x − 36
In this case you know that a=1, b= 5 and c= -36. So the roots can be determined as:
[tex]x1=\frac{-5+\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]
[tex]x1=\frac{-5+\sqrt{25 +144} }{2}[/tex]
[tex]x1=\frac{-5+\sqrt{169} }{2}[/tex]
[tex]x1=\frac{-5+13}{2}[/tex]
[tex]x1=\frac{8}{2}[/tex]
x1= 4
and
[tex]x2=\frac{-5-\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]
[tex]x2=\frac{-5-\sqrt{25 +144} }{2}[/tex]
[tex]x2=\frac{-5-\sqrt{169} }{2}[/tex]
[tex]x2=\frac{-5-13 }{2}[/tex]
[tex]x2=\frac{-18 }{2}[/tex]
x2= -9
Finally, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.
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