Question

How do you find the discriminant and how many solutions does `p^2+12p=-4` have?

Answer 1

A quadratic equation of the form
`ax^2+bx+c=0`
has a discriminant `Delta = b^2-4ac`

The quadratic has:

• no solutions if `Dleta <0`
• 1 solution if `Delta =0`
• 2 solutions if `Delta >0`

Rewriting `p^2+12p=-14`
in a standard form:
`p^2+12p+14=0`

`Delta = (12)^2 - 4(1)(14)`
`= 144 -64`
`=80`

Since `Delta >0`
the given quadratic has
2 solutions