What is the difference in writing a quadratic equation?

Question

The quadratic for the roots 3/7 and 10/3 is -21x²+79x-30.

But is there a difference if it was written as 21x²-79x+30?

Answer 1

Yes, there is a difference!

If f(x) = 21x² -79x + 30, then -f(x) = -21x² + 79x - 30!

f(x) opens upward and goes to +∞as |x| goes to ∞, whereas -f(x) opens downward and goes to -≈ as |x| goes to ∞.

BUT, and this is where you are having trouble, if f(x)=0, then -f(x)=0 too, i.e. they have the same roots as you correctly observe.

I hope this helps!