Question

How do you determine the value of k so that `4x^2 + 24x + k = 0` has discriminant zero?

Answer 1

`k=color(green)(36)`

Explanation:

For the general quadratic: `ax^2+bx+c=0`
the discriminant is
`color(white)("XXX")Delta=b^2-4ac`

For the specific quadratic: `4x^2+24x+k=0`
the discriminant is
`color(white)("XXX")Delta=24^2-4 * 4 * k`

If we want the discriminant to be zero:
`color(white)("XXX")color(blue)(24^2)-color(magenta)(4 * 4 * k) = 0`

`color(white)("XXX")rarr color(blue)((4^2) * (6^2)) - color(magenta)((4^2) * k)=0`

`color(white)("XXX")rarr 6^2-k=0`

`color(white)("XXX")rarr k=6^2=36`