The equation x2 + ax + b = 0, where a and b are different, has solutions x = a and x = b. How many such equations are there?

Pretty sure there's only one, where a=b=0.

For a and b to be solutions you would have to have (x-a)(x-b)=0 which means x^2-(a+b)x+ab=0 which does not match the required form of equation.

(x-a)(x-b)=0

x^2-(a+b) +ab=0

a=-a-b. So b=-2a. and ab=b So a=1

Thus b=-2 one solution as follows

x^2+x-2 =0 = (x‐1)(x+2) thus x=1 or -2