MBA04 wrote:

Q. At how many points does the line y = ax^2 + 2qx + r cut the X-axis.

1) q> r^2

2) 2r > q^2

I do not have the official answer, but hope you can solve this

Answer is E

For any quadratic ax^2+bx+c,

if b^2-4ac >0, then the equation has two real roots (i.e. it cuts the x axis in two distinct points)

if b^2-4ac = 0, then the equation has two real roots that are equal (i.e. it cuts in one distinct point)

if b^2-4ac < 0 then the equation does not have any real roots

Now condition (1) tells us that q>r^2. But this does not tell us whether 4q^2-4ar is >0, =0 or <0 since the value of a in unknown

Condition (2) tells us that 2r>q^2. Again, the value of a is unknown so we cannot arrive at a clear answer to the question.

Together also they do not help.

Hence E