(B) Let the roots of the quadratic equation be $\alpha$ and $\frac{1}{\alpha}$.For a quadratic equation $ax^2 + bx + c = 0$,the product of the roots i

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(B) Let the roots of the quadratic equation be $\alpha$ and $\frac{1}{\alpha}$.For a quadratic equation $ax^2 + bx + c = 0$,the product of the roots is given by $\frac{c}{a}$.Here,$a = 2k + 1$,$b = -(7k + 3)$,and $c = k + 2$.Since the roots are reciprocal,their product is $\alpha \times \frac{1}{\alpha} = 1$.Therefore,$\frac{c}{a} = 1 \Rightarrow \frac{k + 2}{2k + 1} = 1$.Solving for $k$: $k + 2 = 2k + 1$.$2 - 1 = 2k - k$.$k = 1$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Relation between roots and coefficients

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If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

A
$0$
B
$1$
C
$2$
D
$3$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Relation between roots and coefficients

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If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2x^3 - 3x^2 + 6x + 1 = 0$,then $\alpha^2 + \beta^2 + \gamma^2$ is equal to

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If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

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Let $\alpha$ and $\beta$ be the roots of $x^2-6x-2=0$,with $\alpha > \beta$. If $a_n = \alpha^n - \beta^n$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_8}{2a_9}$ is

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