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.
The roots are found by the quadratic formula,
In your equation, , and .
So
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.