SOLUTION: if the roots of x^2-ax+b=0 are real & differ by a quantity which is less than c(c>0),prove that b lies between (1/4)(a^2-c^2)& (1/4)a^2

Question 629643: if the roots of x^2-ax+b=0 are real & differ by a quantity which is less than c(c>0),prove that b lies between (1/4)(a^2-c^2)& (1/4)a^2
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Using the Quadratic Formula on your equation we get:

which simplifies as follows:

which is short for:
or

The difference of these is:

We are told that this difference is less than c, and as is true of any square root, it is not negative. So
and
Squaring both sides of both we get:
and
Now we solve both for b:
and
and

P.S. To me, "between p and q" means "between p and q but not equal to p or q". But I don't think there is any way to eliminate the "or equal to" part of . So the largest possible b would be equal to not between that and .
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