Question

How do you find the discriminant and how many and what type of solutions does `3x^2= -13x - 5` have?

Answer 1

Rewrite the given expression in standard form
`3x^2 = -13x -5`
`rarr 3x^2 +13x +5 = 0`

The discriminant is
`Delta = b^2-4ac`
and for the given equation, has the value
`Delta= 13^2 - 4(3)(5) = 169 - 60 = 109`

`Delta >0`
(but 109 is not a perfect square)
so this equation has
2 Real solutions.