# How many and what type of solutions does the equation have? –4x^2 – 2 = 10x A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions

Mar 11, 2016

2 real roots

#### Explanation:

$y = - 4 {x}^{2} - 10 x - 2 = 0.$ Transform the equation to -->
$y = 2 {x}^{2} + 5 x + 1 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 25 - 8 = 17$ --> $d = \pm \sqrt{17}$
There are 2 real roots;
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} =$
$x = - \frac{5}{4} \pm \frac{\sqrt{7}}{4}$