Question

Use the discriminant, b^2 - 4ac, to determine the number of solutions of the following quadratic equation.: -5x^2 = 5x - 2Then solve the quadratic equation using the formula X = (formula is in the pic attached)

Answer 1

The given equation is,

$-5x^2^{}=5x-2$

Rearranging the equation, we have,

$5x^2+5x-2=0$

Here, a = 5, b = 5, c = -2. Therefore, the discriminant can be calculated as,

$b^2-4ac=5^2+4\times5\times2=65$

The discriminant is 65, and hence it has two distinct real number solutions.

Now, solving for x, we get,

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-5\pm\sqrt[]{65}}{2\times5}=\frac{-1+\sqrt[]{65}}{2},\text{ }\frac{\text{-1-}\sqrt[]{65}}{2}$