1. ## Roots of Quadratic Equation

Which term describes the roots of the equation
2x^2 + 3x - 1 = 0?
(1) rational (3) equal
(2) irrational (4) imaginary

I guessed choice (2) and was right but I still do not know what makes the roots irrational in this case.

2. The roots are found by the quadratic formula, $\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In your equation, $\displaystyle a = 2$, $\displaystyle b = 3$ and $\displaystyle c = -1$.

So $\displaystyle x = \frac{-3 \pm \sqrt{9 + 8}}{4} = \frac{-3 \pm \sqrt{17}}{4}$

This shows there are 2 real roots. Now 17 is a prime number - it can only be divided exactly by 1 and itself. The square root of any prime number is irrational - it cannot be expressed as a fraction. So the roots of the equation are therefore irrational.

3. ## nice....

Originally Posted by nzmathman
The roots are found by the quadratic formula, $\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In your equation, $\displaystyle a = 2$, $\displaystyle b = 3$ and $\displaystyle c = -1$.

So $\displaystyle x = \frac{-3 \pm \sqrt{9 + 8}}{4} = \frac{-3 \pm \sqrt{17}}{4}$

This shows there are 2 real roots. Now 17 is a prime number - it can only be divided exactly by 1 and itself. The square root of any prime number is irrational - it cannot be expressed as a fraction. So the roots of the equation are therefore irrational.
Very nicely explained.