How to solve a quadratic equation by using the discriminant or by factoring?
A quadratic equations is a second-order equation with at most two solutions.The standard form of a quadratic equation looks like: ax2 + bx + c = 0 . For instance if we have the equation x2 - 2x - 35 = 0(where a = 1, b = -2 and c = -35) and if we want to solve it by factoring we need to think about two different numbers that add up to -2 and multiply to give - 35,in order to find out we can either write it as a system of two easy equations a + b = -2 and ab = -35 or simply think about two numbers that satisfy the requirements so we get a = 5 and b = -7.This can be written as (x + 5)(x - 7) = 0 and now we have two smaller equations that we can easily solve: x + 5 = 0 => x1 = -5 and x - 7 = 0 => x2 = 7.We observe that the rootes are exactly the same numbers we thought about but with the opposite sign and this will be the same for any equation. The second way of solving this equation is to use the discriminant which is Δ = √b2−4ac and we use the formula: x1/2=(−b±√b2−4ac) / 2a and we simply replace the a and b in order to find the solutions.After we replace them we will get x1 = -5 and x2 = 7.We can find out the number of rootes we have by observing the discriminant if Δ > 0 => we have two distinct real rootes and if Δ < 0 then we have just one real root.
