Final answer:
The false statement is that if the discriminant is zero, the result will be no real answers. In reality, a zero discriminant indicates one real solution for the quadratic equation.
Step-by-step explanation:
When it comes to solving quadratics with complex solutions, the statement that is FALSE is: If the discriminant is zero, the result will be no real answers.
In fact, when the discriminant (the value under the square root in the quadratic formula) is zero, there is exactly one real solution because the graph of the quadratic function touches the x-axis at one point. The solutions to a quadratic equation ax²+bx+c = 0 can be found using the quadratic formula. The discriminant is calculated using b² - 4ac and it determines the nature of the roots:
- If the discriminant is positive, there are two distinct real solutions, as the quadratic graph cuts the x-axis at two points.
- If the discriminant is zero, there is exactly one real solution, which is when the graph of the equation touches the x-axis at a single point.
- If the discriminant is negative, there are two complex solutions, and the graph does not touch the x-axis at all; instead, the parabola is either above or below the x-axis.
Quadratic equations arising from physical data typically have real roots, and these roots can be graphed on a Two-Dimensional (x-y) Graphing system.