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i have thought : if two line are not parallel then they cross each other ,if we can prove this to line are not parallel ( i don’t know how?) then they intersect each other at some x point. _________________

A would have been the answer provided a=c not equal to zero since, no condition is given hence, we cant its A. and by using both statement together also we cant say whether it will cross or not. if constants are not equal to zero, then the curve will cross each other. if constants(a&C) are zero, then it is line with different value. wont cross each other. and if, constant (all) are zero they will over lap.

so, the best answer is E. _________________

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Attitude determine everything. all the best and God bless you.

Please explain as to how did you get from 2ax^2 + (b-d) = 0 ----> to d=0 - 8a(b-d) >= 0.... and from (a-c)x^2 +(b-a) = 0 -----> to d = 0 - 4(a-c)(b-d) >= 0

This would help me see what I am missing. I understood the explanation but stuck at how the above equation for 'd' was derived.

Please explain as to how did you get from 2ax^2 + (b-d) = 0 ----> to d=0 - 8a(b-d) >= 0.... and from (a-c)x^2 +(b-a) = 0 -----> to d = 0 - 4(a-c)(b-d) >= 0

This would help me see what I am missing. I understood the explanation but stuck at how the above equation for 'd' was derived.

Second d (red part) stands here for the discriminant of a quadratic expression not the variable d.

These are 2 paraboles. Statement 1 (one of the paraboles is inverted depending on a negative or positive) ==> alone insufficient Statement 2 Parobole 1 crosses 0 above Parabole 2 ==> alone insufficient They would cross each other if a was negative. But as this information is not there ==> both statement insufficient

I answered C, which upon further thinking was a careless mistake. To answer the question I tentatively drew out different scenarios for each equation.

With statement 1, the parabola can cross or not cross, it all depends on b and d (insufficient)

With statement 2, we don't have information on a or c, so they can still cross or not cross (insufficient)

When combining to the two statements, I made the mistake of assuming that a was positive and c was negative, which given statement 2, the two lines would not cross. I stupidly forgot about the opposite situation, where statement 1 would still be satisfied, but would give a different result.

2 lines cross when there exists x so that (a-c)x^2=d-b (*) 1) a=-c: don't mention anything about the right side of (*) -> insufficient 2) b>d: if a<c: (*) has at least one root; if a>c: no root -> insufficient Combine 2 stats: still insufficient coz we don't know whether a>c or not