Check the discriminant, which is equal to
(a) 1 - 4b
(b) b^2-4
Now recall what the discriminant means ...
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.
2 answers
if b>2 or b<-2 has 2 roots,
if -2 or 2 1 root,
and if -2<b<2 it has no roots
if -2 or 2 1 root,
and if -2<b<2 it has no roots