If a quadratic equation can be factorised ... It is not possible to find the square root of a negative number, so the equation has no solutions. The graph of \(y = x^2 + 2x + 5\) does not cross ...

Mathematicians once turned up their noses at imaginary numbers. But complex analysis actually simplifies math and physics.

If a quadratic ... one solution to the equation, \( x = 3\). The graph of \(y = x^2 - 6x + 9 \) touches the x-axis at \( x = 3\). It is not possible to find the square root of a negative number ...

However, if you are willing to believe in the existence of square roots of negative numbers, you will get solutions to a whole new set of quadratic equations. In fact, a whole amazing and useful ...