Question 463547
*[tex \LARGE 7x^2 + 4x - 3 = 0]


Know Vieta's formulas, which say that if you have a polynomial


*[tex \LARGE a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 = 0]


Then the sum of the roots is *[tex \LARGE -\frac{a_{n-1}}{a_n}] and the product of the roots is *[tex \LARGE \frac{a_0}{a_n}] (plus, a whole bunch of other identities can be derived but we won't need them here).


Here, the sum of the solutions is -4/7, which is not positive, so I is not true. The product of the solutions is (-3)/7, negative, so II is true. We automatically know III cannot be true since if both solutions were integers, their sum would be an integer, but we already know I is not true. Hence, only II is true; answer is B.


For certain math problems, it can help to find a slick, fast solution. Here we were able to do it without even finding the roots of the quadratic.