Question

(2) Find the quadratic equation whose roots are the reciprocals of the roots
of x^2 + 4x - 10 = 0.​

Answer 1

$\bold{Given:-} \begin{cases} \sf{ \underline{ {x}^{2} + 4x - 10 = 0}} \\ \sf{ \alpha + \beta = \frac{ - b}{a} } \\ \sf{ \alpha \times \beta = \frac{c}{a} } \end {cases}$

${ \bold{\underline{Solution:-}}}$

$Let \: first \: roots \: be \: \alpha \: and \: \frac{1}{ \alpha } .$

$\longrightarrow \: \alpha \times \frac{1}{ \alpha } = \frac{c}{a} \\ \\ \longrightarrow \: \cancel\alpha \times \frac{1}{ \cancel \alpha } = \frac{ - 10}{1} . \\ \\ \longrightarrow \: - 10.$

${ \large{ \boxed{ \underline{ - 10.}}}}$