The product of the roots of the equation
2 − 3 + = 10 is -2 then the
value of k is
Answers
Answer:
One way to solve it is with simple logic: when is the product of two numbers positive? That hapens when either:
both numbers are positive — not just x-3 >0 but you must also have x-5 positive, which means, x > 5;
both numbers are negative — meaning, x < 3
So your x can run from negative infinity to 3 (without ever being 3) and from 5 to positive infinity (without ever being 5). The solution set is written something like this: (−∞,3)U(5,+∞)
(…that really should be the sign for a union of sets, U, but forgot how to get that in Latex)
Another way to think about it is to consider the quadratic function (x− 3) (x− 5) = x2−8x+15 . The coefficient of x2 is positive, that means your function is positive outside the roots (x < 3, x > 5) and negative between the roots. Graph it and have a look; you could use the practice.