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.