Question

How do you find the discriminant and how many solutions does `-5x^2+7x-2=0` have?

Answer 1

Discriminant `D = d^2 = b^2 - 4ac = 49 - 40 = 9` --> d = 3 and d = -3.
There are 2 solutions, called real roots of the quadratic equations.

`x1 = -b/(2a) + d/(2a) = 7/10 - 3/10 = 4/10 = 2/5`

`x2 = -b/2a - d/2a = 7/10 + 3/10 = 10/10 = 1`

Note . We can use shortcut to quickly solve this equation.

Since a + b + c = 0, then one real root is 1 and the other is `(c/a = (-2)/-5 = 2/5)`.
When a - b + c = 0, then one real root is (-1) and the other is `(-c/a)`.