Problem Solving

Hi Vjesus12.

Let's take a look at your question.

Option 1:

Since $$y=x^2-5x+t$$ intersects with the x-axis at (-1,0) we have that $$0=\left(-1\right)^2-5\left(-1\right)+t\ \Leftrightarrow\ 0=1+5+t\ \Leftrightarrow\ t=-6.$$ Hence, the curve is represented by $$y=x^2-5x-6,$$ and this cuadratic equation has to roots, $$x_1=-1\ \left(\text{already}\ \text{known}\right)\ and\ \ \ \ \ x_2=6.$$ Therefore, the curve intersects with the x-axis at (6,0).

This is why the correct answer is D.

Option 2:

Since $$y=x^2-5x+t$$ we have that $$\ x^2-5x+t=\left(x-x_1\right)\left(x-x_2\right).$$ We already know that x_1=-1. Therefore, $$x^2-5x+t=\left(x+1\right)\left(x-x_2\right)\ and\ \ \left(\ 1-x_2=-5\ and\ \ 1\cdot (-x_2)=-x_2=t\right)$$ and therefore $$x_2=6.$$ Therefore, the curve intersects with the x-axis at (6,0).

I hope this answer can help you.

I'm available if you'd like a follow-up.

Regards.