Question

What does the graph of f(x)=(3x-5)(x+9) cross the x axis

Answer 1

Hello.

Firstly, we need to simplify the function:

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

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

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

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

Hope I helped.