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.

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- Jan 4th 2009, 12:51 PMmagentaritaRoots of Quadratic Equation
Which term describes the roots of the equation

2*x^*2 + 3*x*- 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. - Jan 4th 2009, 01:05 PMnzmathman
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. - Jan 5th 2009, 09:53 PMmagentaritanice....