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CAT 2025 Lesson : Quadratic Equations - Past Questions

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11. Past Questions

Question 1

Let xx = 4+4−4+4−... to infinity\sqrt{4+\sqrt{4 - \sqrt{4 + \sqrt{4 - ... \space \mathrm{to \ infinity}}}}}. Then xx equals
[CAT 2005]

3
13−12\dfrac{\sqrt13 - 1}{2}
13+12\dfrac{\sqrt13 + 1}{2}
13\sqrt13

Question 2

If 0<p<10 < p< 1, then roots of the equation (1−p)x2+4x+p=0(1 - p)x^2 + 4x + p = 0 are
[XAT 2008]

Both 0
Imaginary
Real and both positive
Real and of opposite sign
Real and both negative

Question 3

If one root of the equation ax2+bx+c=0ax^2 + bx + c = 0 is double of the other, then 2b22b^2 =
[IIFT 2008]

9ac9 ac
c2ac \sqrt2a
23ac2 \sqrt3ac
None of the above

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