New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2011 · Shift 1 · Q27

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Quadratic Equation and Inequalities
2011 · Shift 1 · Q27

Quadratic Equation and Inequalities question

2011 · Shift 1 · Q27

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\alpha

and

\beta

be the roots of

{x^2} - 6x - 2 = 0,

with

\alpha \gt \beta .

If

{a_n} = {\alpha ^n} - {\beta ^n}

for

\,n \ge 1

then the value of

{{{a_{10}} - 2{a_8}} \over {2{a_9}}}

is

A
1
B
2
C
3
D
4

More from Quadratic Equation and Inequalities

Let $(x_{0}, y_{0})$ be the solution of the following equations $(2 x)^{ℓ n 2} = (3 y)^{ℓ n 3} 3^{ℓ n x} = 2^{ℓ n y}$ Then $x_{0}$ …2011 · MCQ
The number of distinct real roots of $x^{4} - 4 x^{3} + 12 x^{2} + x - 1 = 0$ 2011 · Numerical
A value of $b$ for which the equations $x^{2} + b x - 1 = 0 x^{2} + x + b = 0$ have one root in common is2011 · MCQ
Let $p$ and $q$ be real numbers such that $p e 0, p^{3} e q$ and $p^{3} e - q .$ If $p^{3} e - q .$ and $β$ are nonzero complex numbers satisfying $α + β = - p$ and $α^{3} + β^{3} = q,$ then a quadratic…2010 · MCQ
The smallest value of $k$ , for which both the roots of the equation $x^{2} - 8 k x + 16 (k^{2} - k + 1) = 0$ are real, distinct and have values at least 4, is2009 · Numerical
Let $a, b, c$ , $p, q$ be real numbers. Suppose $α, β$ are the roots of the equation $x^{2} + 2 p x + q = 0$ and $α, \frac{1}{β}$ are the roots of the equation $a x^{2} + 2 b x + c = 0,$ where $β^{2} \in {- 1, 0, 1}$ …2008 · MCQ
Let $α, β$ be the roots of the equation $x^{2} - p x + r = 0$ and $\frac{α}{2}, 2 β$ be the roots of the equation $x^{2} - q x + r = 0$ . Then the value of r is2007 · MCQ
Let $R$ denote the set of all real numbers. Let $a_{i}, b_{i} \in R$ for $i \in {1, 2, 3}$ . Define the functions $f : R \to R$ , $g : R \to R$ , and $h : R \to R$ by $f (x) = a_{1} + 10 x + a_{2} x^{2} + a_{3} x^{3} + x^{4} g (x) = b_{1} + 3 x + b_{2} x^{2} + b_{3} x^{3} + x^{4} h (x) = f (x + 1) - g (x + 2)$ …2025 · MCQ