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

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Answer 1 · 2015-04-29T15:26:24

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.

How do you find the discriminant and how many and what type of solutions does 3x^2= -13x - 53x^2= -13x - 5 have?