Let D be the absolute value of the difference of the 2 roots of the equation 3x^2-10x-201=0. Find [D]. [x] denotes the greatest integer less than or equal to x.
I came across this question in a Math Competition and I am not sure how to solve it without using a calculator, since calculators are not allowed in the competition. Thanks.
Best Answer
Hint: If $a, b$ are the roots, $$|a-b|^2 = (a-b)^2 = (a+b)^2 - 4 ab = \frac{100}9+4\times \frac{201}3 = \frac{2512}9$$