Question

How many x intercepts does this parabola have? 6x^2-4x-3 How many x intercepts does this parabola have? 6x^2-4x-3 @Mathematics

Answer 1

Two right?

Answer 2

right

Answer 3

\[b^2-4ac=(-4)^2-4(6)(-3)>0 => \text{ so yes two x-intercepts}\]

Answer 4

the roots of a quadratic of the form:\[ax^2+bx+c=0\]are given by:\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]so, for it to intercept the x-axis, the roots must be real, which implies:\[b^2-4ac>=0\]as @myininaya showed above.

Answer 5

think of the question as:\[y=6x^2-4x-3\]for this to intercept the x-axis, y must be zero, which leads to trying to show:\[6x^2-4x-3=0\]as no imaginary roots.

Answer 6

Alright, thats similiar to what I was doing thanks