Question 232608
The general form of a quadratic equation:
{{{ax^2 + bx  + c = 0}}}
The quadratic formula:
{{{x = (-b +- sqrt(b^2 -4ac))/(2a)}}}<br>
The expression inside the square root, {{{b^2-4ac}}}, is called the discriminant. It is called this because its value determines whether there are 0, 1 or 2 real roots. This is how it works:<ul><li>The discriminant is a positive number (any positive number. Since the discriminant is inside the square root we will find the square root of the discriminant. The square root of a positive number is another positive number. And since this  square root is both added to and subtracted from -b in the numerator, we will end up with 2 real roots: one when we add the square root and one when we subtract.</li><li>The discriminant is zero. The square root of zero is zero. And whether you add zero to -b or subtract zero from -b you end up with the same thing, -b. This is when we get 1 real root.</li><li>The discriminant is a negative number (any negative number). Since it is impossible to square a real number and get a negative number, the square root of any negative number does not exist within the set of Real numbers. This is when we get no real roots.</li></ul>
Using this on you equation...
Find the value of the discriminant:
{{{b^2 - 4ac = (-3)^2 - 4(1)(8) = 9 - 32 = -23}}}
The discriminant is a negative number so there are no real roots.