Question

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

Answer 1

Let y = 0
what value do you need to complete the square ?

Answer 2

x-intercepts when y = 0

Answer 3

A quadratic polynomial has two roots when it can be factored from \(ax^2+bx+c\) to \(a(x-r_1)(x-r_2)\). This happens when the discriminant, \(\Delta=b^2-4ac\), is positive.

The discriminant here is \(49-12m\). What values of \(m\) make this positive? In other words, solve \(49-12m>0\).