How to tell if a quadratic equation has a real solution?
Mathematics · High School · Tue Nov 03 2020
Answered on
The quadratic equation is often solve using the quadratic formula represented as,
x = −b ± √(b^2 − 4ac)/2a
where a ≠ 0, in the form
ax^2+bx+c=0
When b^2−4ac = 0 there is one real root.
When b^2−4ac > 0 there are two real roots.
When b^2−4ac < 0 there are no real roots, only a complex number.
Hence, In order to tell if the quadratic formula has a real solution, b^2 - 4ac must not result to a negative number since, we cannot take the square root of a negative number. Taking the square root of a negative number would result to an imaginary number, and x would result to an imaginary or complex number.