Question

For what values of k does the graph of y=5x^2 + kx + 1 have:

a. One x-intercept
b. two x-intercepts
c. No x-intercepts

Answer 1

work with the discriminant b^2 - 4ac

if b^2 - 4ac = 0 you have one x-intercept
if b^2 - 4ac > 0 you have two x-intercepts
if b^2 - 4ac < 0 you have no x-intercepts

I will do the 2nd one, you do the other cases

for 5x^2 + kx + 1,
a = 5, b = k, c = 1
k^2 - 4(5)(1) > 0
k^2 > 20
k > √20 OR k < -√20