Question

Use graph of the function f(x)=x2 to find how the number of roots of the equation depends on the value of b.

a)x^2=x−b

If b < ANSWER, the equation has 2 roots.
If b = ANSWER, the equation has 1 root.
If b > ANSWER, the equation has no roots.

b) x^2=bx−1


If b is on the interval ( , ) ∪ ( , ), the equation has two roots.
If b equals to , , the equation has one root.
If b is on the interval ( , ), the equation has no roots.

Answer 1

Check the discriminant, which is equal to
(a) 1 - 4b
(b) b^2-4
Now recall what the discriminant means ...

Answer 2

if b>2 or b<-2 has 2 roots,
if -2 or 2 1 root,
and if -2<b<2 it has no roots