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*5*2=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*5}=\frac{-1+\sqrt[]{65}}{2},\text{ }\frac{\text{-1-}\sqrt[]{65}}{2}`