Question

Write a quadratic inequality whose solution is x < 3 or x > 7

I know the formula and everything, but I'm not sure where to move on from the inequality formula (x-a)(x-b)>0 Can someone please explain, am I supposed to use the standard form first?

Answer 1

If you recall how a parabola looks, you know that if the leading coefficient is positive, then y is negative between the roots. So, you want
(x-3)(x-7) > 0
That is really all you need. You can expand that to
x^2 - 10x + 21 > 0
but that's just busy work.