Question

Whats an example of a quadratic equation that cannot be factored with a real solution?

Answer 1

Answer:

Step-by-step explanation:

The key here is the "discriminant."  That's b^2 - 4ac, where a, b and c are the coefficients of the quadratic.

If the discriminant turns out to be positive, we have two real, different roots.

If the discriminant turns out to be zero, we have two real, equal roots.

Finally, if the discriminant turns out to be negative, we have two complex, different roots.  

Just supposing that a = 1 and b = 2, the discriminant would be

2^2 - 4(1)c.  Set this equal to 0 and solve for c:  4 - 4c = 0, or c = 1.  If c is greater than 1, the discriminant will be negative and we will have two comlex, different roots.