Question

If zeroes of polynomial 2x^2-3x+lambda and ax^2-6x+u are same tgen find tge value of :lambda×a/u

Answer 1

$\textbf{Given:}$

$\textsf{Zeroes of polynmials}$

$\mathsf{2x^2-3x+\lambda\;and\;ax^2-6x+u\;are\;same}$

$\textbf{To find:}$

$\textsf{The value of}\;\mathsf{\lambda{\times}\dfrac{a}{u}}$

$\textbf{Solution:}$

$\mathsf{Product\;of\;zeroes\;of\;2x^2-3x+\lambda\;is\;\dfrac{\lambda}{2}}$

$\mathsf{Product\;of\;zeroes\;of\;ax^2-6x+u\;is\;\dfrac{u}{a}}$

$\textsf{Since the zeroes of the given polynomials are same, we have}$

$\textsf{product of zeroes the corresponding polynomials also equal}$

$\implies\mathsf{\dfrac{\lambda}{2}=\dfrac{u}{a}}$

$\implies\boxed{\mathsf{\lambda{\times}\dfrac{a}{u}=2}}$

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