Respuesta :

guipocas
Hello.

Firstly, we need to simplify the function:

[tex]\mathsf{f(x) = (3x - 5) \times (x + 9)} \\
\\
\mathsf{f(x) = 3x^{2} - 5x + 27x - 45} \\
\\
\mathsf{f(x) = 3x^{2} + 22x - 45}[/tex]

The graph crosses the 'x' axis when y = 0. Ergo:

[tex]\mathsf{3x^{2} + 22x - 45 = 0} \\
\\
\\
\mathsf{\triangle = b^{2} - 4ac} \\
\\
\mathsf{\triangle = 484 - 4 \times 3 \times (-45)} \\
\\
\mathsf{\triangle = 484 + 540} \\
\\
\mathsf{\triangle = 1024} \\
\\
\\
\mathsf{x = \dfrac{-b \pm \sqrt{\triangle}}{2a}} \\
\\
\\
\mathsf{x_{1} = \dfrac{-22 + 32}{6} = \dfrac{10}{6} = \dfrac{5}{3}} \\
\\
\\
\mathsf{x_{2} = \dfrac{-22 - 32}{6} = \dfrac{-54}{6} = -9}[/tex]

Therefore, the graph crosses the x axis when x = -9 and 5/3.

Hope I helped.

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