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Quadratic Equations

Quadratic Equations

MODULES

Basics of Polynomial & Quadratic Equations
Discriminant & Graphical Representation
Sum & Product of Roots
Factorisation Method
Formulation & Completion of Squares
Changes to Roots
Mistakes in Roots, Common Roots & Squaring
Infinite Series & Transposed
Other Types
Higher Order Equations
Synthetic Division & Remainder Theorem
Maxima, Minima & Descrates Rule
Past Questions

CONCEPTS & CHEATSHEET

Concept Revision Video

SPEED CONCEPTS

Quadratic Equations 1
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Quadratic Equations 2
-/10
Quadratic Equations 3
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PRACTICE

Quadratic Equations : Level 1
Quadratic Equations : level 2
Quadratic Equations : level 3
ALL MODULES

CAT 2025 Lesson : Quadratic Equations - Past Questions

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11. Past Questions

Question 1

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

3
13−12\dfrac{\sqrt13 - 1}{2}21​3−1​
13+12\dfrac{\sqrt13 + 1}{2}21​3+1​
13\sqrt131​3

Answer: (3) 13+12\dfrac{\sqrt13 + 1}{2}21​3+1​

Question 2

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

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

Answer: (5) Real and both negative

Question 3

If one root of the equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 is double of the other, then 2b22b^22b2 =
[IIFT 2008]

9ac9 ac9ac
c2ac \sqrt2ac2​a
23ac2 \sqrt3ac23​ac
None of the above

Answer: (1) 9ac9 ac9ac

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