Question

In the quadratic equation, a b c are rational numbers. The quadratic has 2 distinct zeros. One of the zeros is rational. What does this say about the other

Answer 1

Answer:

The other zero is also a rational number.

Step-by-step explanation:

In a quadratic equation

$ax^2+bx+c=0$

Quadratic formula:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Case 1: If $b^2-4ac>0$, then the given quadratic equation has two distinct real zeros.

Case 2: If $b^2-4ac=0$, then the given quadratic equation has exactly one real zero.

Case 3: If $b^2-4ac$, then the given quadratic equation has two distinct complex zeros.

It is given that the quadratic has 2 distinct zeros. One of the zeros is rational.

It means

$b^2-4ac>0$ and $\sqrt{b^2-4ac}$ is a rational number.

Therefore, the other zero is also a rational number.